5x^2-4x=3x^2+x

Solution for 5x^2-4x=3x^2+x equation:

5x^2-4x=3x^2+x

We move all terms to the left:

5x^2-4x-(3x^2+x)=0

We get rid of parentheses

5x^2-3x^2-4x-x=0

We add all the numbers together, and all the variables

2x^2-5x=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$