x2-12(12-x)=7x+3(8-x)-8

Solution for x2-12(12-x)=7x+3(8-x)-8 equation:

x2-12(12-x)=7x+3(8-x)-8

We move all terms to the left:

x2-12(12-x)-(7x+3(8-x)-8)=0

We add all the numbers together, and all the variables

x2-12(-1x+12)-(7x+3(-1x+8)-8)=0

We add all the numbers together, and all the variables

x^2-12(-1x+12)-(7x+3(-1x+8)-8)=0

We multiply parentheses

x^2+12x-(7x+3(-1x+8)-8)-144=0


We calculate terms in parentheses: -(7x+3(-1x+8)-8), so:

7x+3(-1x+8)-8

We multiply parentheses

7x-3x+24-8

We add all the numbers together, and all the variables

4x+16

Back to the equation:

-(4x+16)


We get rid of parentheses

x^2+12x-4x-16-144=0

We add all the numbers together, and all the variables

x^2+8x-160=0

a = 1; b = 8; c = -160;
Δ = b2-4ac
Δ = 82-4·1·(-160)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{11}}{2*1}=\frac{-8-8\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{11}}{2*1}=\frac{-8+8\sqrt{11}}{2}
$