3x(x-3)=5x2-10x

Solution for 3x(x-3)=5x2-10x equation:

3x(x-3)=5x^2-10x

We move all terms to the left:

3x(x-3)-(5x^2-10x)=0

We multiply parentheses

3x^2-9x-(5x^2-10x)=0

We get rid of parentheses

3x^2-5x^2-9x+10x=0

We add all the numbers together, and all the variables

-2x^2+x=0

a = -2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-2)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-2}=\frac{0}{-4}
=0
$