.9x(x-20)=830

Solution for .9x(x-20)=830 equation:

.9x(x-20)=830

We move all terms to the left:

.9x(x-20)-(830)=0

We multiply parentheses

x^2-20x-830=0

a = 1; b = -20; c = -830;
Δ = b2-4ac
Δ = -202-4·1·(-830)
Δ = 3720
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:

$\sqrt{\Delta}=\sqrt{3720}=\sqrt{4*930}=\sqrt{4}*\sqrt{930}=2\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{930}}{2*1}=\frac{20-2\sqrt{930}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{930}}{2*1}=\frac{20+2\sqrt{930}}{2}
$