5x^2+3x=3x^2+20

Solution for 5x^2+3x=3x^2+20 equation:

5x^2+3x=3x^2+20

We move all terms to the left:

5x^2+3x-(3x^2+20)=0

We get rid of parentheses

5x^2-3x^2+3x-20=0

We add all the numbers together, and all the variables

2x^2+3x-20=0

a = 2; b = 3; c = -20;
Δ = b2-4ac
Δ = 32-4·2·(-20)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*2}=\frac{10}{4}
=2+1/2
$