(2x-5)(2x)=113

Solution for (2x-5)(2x)=113 equation:

(2x-5)(2x)=113

We move all terms to the left:

(2x-5)(2x)-(113)=0

We multiply parentheses

4x^2-10x-113=0

a = 4; b = -10; c = -113;
Δ = b2-4ac
Δ = -102-4·4·(-113)
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{53}}{2*4}=\frac{10-6\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{53}}{2*4}=\frac{10+6\sqrt{53}}{8}
$