.5x(2x-5)=20

Solution for .5x(2x-5)=20 equation:

.5x(2x-5)=20

We move all terms to the left:

.5x(2x-5)-(20)=0

We multiply parentheses

2x^2-5x-20=0

a = 2; b = -5; c = -20;
Δ = b2-4ac
Δ = -52-4·2·(-20)
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{185}}{2*2}=\frac{5-\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*2}=\frac{5+\sqrt{185}}{4}
$