(x+20)(3x-10)=90

Solution for (x+20)(3x-10)=90 equation:

(x+20)(3x-10)=90

We move all terms to the left:

(x+20)(3x-10)-(90)=0

We multiply parentheses ..

(+3x^2-10x+60x-200)-90=0

We get rid of parentheses

3x^2-10x+60x-200-90=0

We add all the numbers together, and all the variables

3x^2+50x-290=0

a = 3; b = 50; c = -290;
Δ = b2-4ac
Δ = 502-4·3·(-290)
Δ = 5980
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:

$\sqrt{\Delta}=\sqrt{5980}=\sqrt{4*1495}=\sqrt{4}*\sqrt{1495}=2\sqrt{1495}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{1495}}{2*3}=\frac{-50-2\sqrt{1495}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{1495}}{2*3}=\frac{-50+2\sqrt{1495}}{6}
$