2x+3=(1/2)(5x-14)

Solution for 2x+3=(1/2)(5x-14) equation:

2x+3=(1/2)(5x-14)

We move all terms to the left:

2x+3-((1/2)(5x-14))=0


Domain of the equation: 2)(5x-14))!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/2)(5x-14))+3=0

We multiply parentheses ..

-((+5x^2+1/2*-14))+2x+3=0

We multiply all the terms by the denominator


-((+5x^2+1+2x*2*-14))+3*2*-14))=0


We calculate terms in parentheses: -((+5x^2+1+2x*2*-14)), so:

(+5x^2+1+2x*2*-14)

We get rid of parentheses

5x^2+2x*2*+1-14

We add all the numbers together, and all the variables

5x^2+2x*2*-13

Wy multiply elements

5x^2+4x^2-13

We add all the numbers together, and all the variables

9x^2-13

Back to the equation:

-(9x^2-13)


We add all the numbers together, and all the variables

-(9x^2-13)=0

We get rid of parentheses

-9x^2+13=0

a = -9; b = 0; c = +13;
Δ = b2-4ac
Δ = 02-4·(-9)·13
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{13}}{2*-9}=\frac{0-6\sqrt{13}}{-18}
=-\frac{6\sqrt{13}}{-18}
=-\frac{\sqrt{13}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{13}}{2*-9}=\frac{0+6\sqrt{13}}{-18}
=\frac{6\sqrt{13}}{-18}
=\frac{\sqrt{13}}{-3}
$