15x=3x^2-150

Solution for 15x=3x^2-150 equation:

15x=3x^2-150

We move all terms to the left:

15x-(3x^2-150)=0

We get rid of parentheses

-3x^2+15x+150=0

a = -3; b = 15; c = +150;
Δ = b2-4ac
Δ = 152-4·(-3)·150
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*-3}=\frac{-60}{-6}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*-3}=\frac{30}{-6}
=-5
$