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

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

X^2+5X-3=2X+5

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+3X-8=0

a = 1; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·1·(-8)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{41}}{2*1}=\frac{-3-\sqrt{41}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{41}}{2*1}=\frac{-3+\sqrt{41}}{2}
$