(2x-98)(2x-72)=90

Solution for (2x-98)(2x-72)=90 equation:

(2x-98)(2x-72)=90

We move all terms to the left:

(2x-98)(2x-72)-(90)=0

We multiply parentheses ..

(+4x^2-144x-196x+7056)-90=0

We get rid of parentheses

4x^2-144x-196x+7056-90=0

We add all the numbers together, and all the variables

4x^2-340x+6966=0

a = 4; b = -340; c = +6966;
Δ = b2-4ac
Δ = -3402-4·4·6966
Δ = 4144
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:

$\sqrt{\Delta}=\sqrt{4144}=\sqrt{16*259}=\sqrt{16}*\sqrt{259}=4\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-4\sqrt{259}}{2*4}=\frac{340-4\sqrt{259}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+4\sqrt{259}}{2*4}=\frac{340+4\sqrt{259}}{8}
$