4x2-20x=-18

Solution for 4x2-20x=-18 equation:

4x^2-20x=-18

We move all terms to the left:

4x^2-20x-(-18)=0

We add all the numbers together, and all the variables

4x^2-20x+18=0

a = 4; b = -20; c = +18;
Δ = b2-4ac
Δ = -202-4·4·18
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{7}}{2*4}=\frac{20-4\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{7}}{2*4}=\frac{20+4\sqrt{7}}{8}
$