(4x-5)(4x+3)=902

Solution for (4x-5)(4x+3)=902 equation:

(4x-5)(4x+3)=902

We move all terms to the left:

(4x-5)(4x+3)-(902)=0

We multiply parentheses ..

(+16x^2+12x-20x-15)-902=0

We get rid of parentheses

16x^2+12x-20x-15-902=0

We add all the numbers together, and all the variables

16x^2-8x-917=0

a = 16; b = -8; c = -917;
Δ = b2-4ac
Δ = -82-4·16·(-917)
Δ = 58752
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:

$\sqrt{\Delta}=\sqrt{58752}=\sqrt{576*102}=\sqrt{576}*\sqrt{102}=24\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24\sqrt{102}}{2*16}=\frac{8-24\sqrt{102}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24\sqrt{102}}{2*16}=\frac{8+24\sqrt{102}}{32}
$