5x^2=15x+90

Solution for 5x^2=15x+90 equation:

5x^2=15x+90

We move all terms to the left:

5x^2-(15x+90)=0

We get rid of parentheses

5x^2-15x-90=0

a = 5; b = -15; c = -90;
Δ = b2-4ac
Δ = -152-4·5·(-90)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-45}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+45}{2*5}=\frac{60}{10}
=6
$