4x(x-5)=92

Solution for 4x(x-5)=92 equation:

4x(x-5)=92

We move all terms to the left:

4x(x-5)-(92)=0

We multiply parentheses

4x^2-20x-92=0

a = 4; b = -20; c = -92;
Δ = b2-4ac
Δ = -202-4·4·(-92)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{13}}{2*4}=\frac{20-12\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{13}}{2*4}=\frac{20+12\sqrt{13}}{8}
$