x2+x+23=-8x+3

Solution for x2+x+23=-8x+3 equation:

x2+x+23=-8x+3

We move all terms to the left:

x2+x+23-(-8x+3)=0

We add all the numbers together, and all the variables

x^2+x-(-8x+3)+23=0

We get rid of parentheses

x^2+x+8x-3+23=0

We add all the numbers together, and all the variables

x^2+9x+20=0

a = 1; b = 9; c = +20;
Δ = b2-4ac
Δ = 92-4·1·20
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-1}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+1}{2*1}=\frac{-8}{2}
=-4
$