2x^2-6x=7x-20

Solution for 2x^2-6x=7x-20 equation:

2x^2-6x=7x-20

We move all terms to the left:

2x^2-6x-(7x-20)=0

We get rid of parentheses

2x^2-6x-7x+20=0

We add all the numbers together, and all the variables

2x^2-13x+20=0

a = 2; b = -13; c = +20;
Δ = b2-4ac
Δ = -132-4·2·20
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{-(-13)-3}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*2}=\frac{16}{4}
=4
$