2x^2+5x+3=x^2+x+15

Solution for 2x^2+5x+3=x^2+x+15 equation:

2x^2+5x+3=x^2+x+15

We move all terms to the left:

2x^2+5x+3-(x^2+x+15)=0

We get rid of parentheses

2x^2-x^2+5x-x-15+3=0

We add all the numbers together, and all the variables

x^2+4x-12=0

a = 1; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·1·(-12)
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{-(4)-8}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*1}=\frac{4}{2}
=2
$