7x(x+20)=90

Solution for 7x(x+20)=90 equation:

7x(x+20)=90

We move all terms to the left:

7x(x+20)-(90)=0

We multiply parentheses

7x^2+140x-90=0

a = 7; b = 140; c = -90;
Δ = b2-4ac
Δ = 1402-4·7·(-90)
Δ = 22120
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:

$\sqrt{\Delta}=\sqrt{22120}=\sqrt{4*5530}=\sqrt{4}*\sqrt{5530}=2\sqrt{5530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-2\sqrt{5530}}{2*7}=\frac{-140-2\sqrt{5530}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+2\sqrt{5530}}{2*7}=\frac{-140+2\sqrt{5530}}{14}
$