-45x^2+15x^2=10x

Solution for -45x^2+15x^2=10x equation:

-45x^2+15x^2=10x

We move all terms to the left:

-45x^2+15x^2-(10x)=0

We add all the numbers together, and all the variables

-30x^2-10x=0

a = -30; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-30)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-30}=\frac{20}{-60}
=-1/3
$