5x^2-10x+2=3x^2+x-7

Solution for 5x^2-10x+2=3x^2+x-7 equation:

5x^2-10x+2=3x^2+x-7

We move all terms to the left:

5x^2-10x+2-(3x^2+x-7)=0

We get rid of parentheses

5x^2-3x^2-10x-x+7+2=0

We add all the numbers together, and all the variables

2x^2-11x+9=0

a = 2; b = -11; c = +9;
Δ = b2-4ac
Δ = -112-4·2·9
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-7}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+7}{2*2}=\frac{18}{4}
=4+1/2
$