X^2+5x+23=8-3x

Solution for X^2+5x+23=8-3x equation:

X^2+5X+23=8-3X

We move all terms to the left:

X^2+5X+23-(8-3X)=0

We add all the numbers together, and all the variables

X^2+5X-(-3X+8)+23=0

We get rid of parentheses

X^2+5X+3X-8+23=0

We add all the numbers together, and all the variables

X^2+8X+15=0

a = 1; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*1}=\frac{-6}{2}
=-3
$