(3x-8)-(4x-6)+(5x-2)(5x+2)=96

Solution for (3x-8)-(4x-6)+(5x-2)(5x+2)=96 equation:

(3x-8)-(4x-6)+(5x-2)(5x+2)=96

We move all terms to the left:

(3x-8)-(4x-6)+(5x-2)(5x+2)-(96)=0

We use the square of the difference formula

25x^2+(3x-8)-(4x-6)-4-96=0

We get rid of parentheses

25x^2+3x-4x-8+6-4-96=0

We add all the numbers together, and all the variables

25x^2-1x-102=0

a = 25; b = -1; c = -102;
Δ = b2-4ac
Δ = -12-4·25·(-102)
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-101}{2*25}=\frac{-100}{50}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+101}{2*25}=\frac{102}{50}
=2+1/25
$