3x=2x^2-5x^2

Solution for 3x=2x^2-5x^2 equation:

3x=2x^2-5x^2

We move all terms to the left:

3x-(2x^2-5x^2)=0

We get rid of parentheses

-2x^2+5x^2+3x=0

We add all the numbers together, and all the variables

3x^2+3x=0

a = 3; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·3·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*3}=\frac{0}{6}
=0
$