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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+2x-5=0

a = 3; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·3·(-5)
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{-(2)-8}{2*3}=\frac{-10}{6}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8}{2*3}=\frac{6}{6}
=1
$