-2x2+5x+23=-x2+3x+15

Solution for -2x2+5x+23=-x2+3x+15 equation:

-2x^2+5x+23=-x2+3x+15

We move all terms to the left:

-2x^2+5x+23-(-x2+3x+15)=0

We add all the numbers together, and all the variables

-2x^2-(-1x^2+3x+15)+5x+23=0

We get rid of parentheses

-2x^2+1x^2-3x+5x-15+23=0

We add all the numbers together, and all the variables

-1x^2+2x+8=0

a = -1; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-1}=\frac{4}{-2}
=-2
$