4x(x-5)=18

Solution for 4x(x-5)=18 equation:

4x(x-5)=18

We move all terms to the left:

4x(x-5)-(18)=0

We multiply parentheses

4x^2-20x-18=0

a = 4; b = -20; c = -18;
Δ = b2-4ac
Δ = -202-4·4·(-18)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{43}}{2*4}=\frac{20-4\sqrt{43}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{43}}{2*4}=\frac{20+4\sqrt{43}}{8}
$