3x-10=(1/4)(8x+12)

Solution for 3x-10=(1/4)(8x+12) equation:

3x-10=(1/4)(8x+12)

We move all terms to the left:

3x-10-((1/4)(8x+12))=0


Domain of the equation: 4)(8x+12))!=0

x∈R


We add all the numbers together, and all the variables

3x-((+1/4)(8x+12))-10=0

We multiply parentheses ..

-((+8x^2+1/4*12))+3x-10=0

We multiply all the terms by the denominator


-((+8x^2+1+3x*4*12))-10*4*12))=0


We calculate terms in parentheses: -((+8x^2+1+3x*4*12)), so:

(+8x^2+1+3x*4*12)

We get rid of parentheses

8x^2+3x*4*12+1

Wy multiply elements

8x^2+144x*1+1

Wy multiply elements

8x^2+144x+1

Back to the equation:

-(8x^2+144x+1)


We add all the numbers together, and all the variables

-(8x^2+144x+1)=0

We get rid of parentheses

-8x^2-144x-1=0

a = -8; b = -144; c = -1;
Δ = b2-4ac
Δ = -1442-4·(-8)·(-1)
Δ = 20704
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:

$\sqrt{\Delta}=\sqrt{20704}=\sqrt{16*1294}=\sqrt{16}*\sqrt{1294}=4\sqrt{1294}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-4\sqrt{1294}}{2*-8}=\frac{144-4\sqrt{1294}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+4\sqrt{1294}}{2*-8}=\frac{144+4\sqrt{1294}}{-16}
$