((5x-6)(5x-6))=x+8

Solution for ((5x-6)(5x-6))=x+8 equation:

((5x-6)(5x-6))=x+8

We move all terms to the left:

((5x-6)(5x-6))-(x+8)=0

We get rid of parentheses

((5x-6)(5x-6))-x-8=0

We multiply parentheses ..

((+25x^2-30x-30x+36))-x-8=0


We calculate terms in parentheses: +((+25x^2-30x-30x+36)), so:

(+25x^2-30x-30x+36)

We get rid of parentheses

25x^2-30x-30x+36

We add all the numbers together, and all the variables

25x^2-60x+36

Back to the equation:

+(25x^2-60x+36)


We add all the numbers together, and all the variables

-1x+(25x^2-60x+36)-8=0

We get rid of parentheses

25x^2-1x-60x+36-8=0

We add all the numbers together, and all the variables

25x^2-61x+28=0

a = 25; b = -61; c = +28;
Δ = b2-4ac
Δ = -612-4·25·28
Δ = 921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-\sqrt{921}}{2*25}=\frac{61-\sqrt{921}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{921}}{2*25}=\frac{61+\sqrt{921}}{50}
$