X2-5x=3x-3x2

Solution for X2-5x=3x-3x2 equation:

X2-5X=3X-3X^2

We move all terms to the left:

X2-5X-(3X-3X^2)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4X^2-8X=0

a = 4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·4·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*4}=\frac{16}{8}
=2
$