10x-24-3x=(1/2)(14x-24)

Solution for 10x-24-3x=(1/2)(14x-24) equation:

10x-24-3x=(1/2)(14x-24)

We move all terms to the left:

10x-24-3x-((1/2)(14x-24))=0


Domain of the equation: 2)(14x-24))!=0

x∈R


We add all the numbers together, and all the variables

10x-3x-((+1/2)(14x-24))-24=0

We add all the numbers together, and all the variables

7x-((+1/2)(14x-24))-24=0

We multiply parentheses ..

-((+14x^2+1/2*-24))+7x-24=0

We multiply all the terms by the denominator


-((+14x^2+1+7x*2*-24))-24*2*-24))=0


We calculate terms in parentheses: -((+14x^2+1+7x*2*-24)), so:

(+14x^2+1+7x*2*-24)

We get rid of parentheses

14x^2+7x*2*+1-24

We add all the numbers together, and all the variables

14x^2+7x*2*-23

Wy multiply elements

14x^2+14x^2-23

We add all the numbers together, and all the variables

28x^2-23

Back to the equation:

-(28x^2-23)


We add all the numbers together, and all the variables

-(28x^2-23)=0

We get rid of parentheses

-28x^2+23=0

a = -28; b = 0; c = +23;
Δ = b2-4ac
Δ = 02-4·(-28)·23
Δ = 2576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2576}=\sqrt{16*161}=\sqrt{16}*\sqrt{161}=4\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{161}}{2*-28}=\frac{0-4\sqrt{161}}{-56}
=-\frac{4\sqrt{161}}{-56}
=-\frac{\sqrt{161}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{161}}{2*-28}=\frac{0+4\sqrt{161}}{-56}
=\frac{4\sqrt{161}}{-56}
=\frac{\sqrt{161}}{-14}
$