X^2+19x+15=8x-3

Solution for X^2+19x+15=8x-3 equation:

X^2+19X+15=8X-3

We move all terms to the left:

X^2+19X+15-(8X-3)=0

We get rid of parentheses

X^2+19X-8X+3+15=0

We add all the numbers together, and all the variables

X^2+11X+18=0

a = 1; b = 11; c = +18;
Δ = b2-4ac
Δ = 112-4·1·18
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*1}=\frac{-4}{2}
=-2
$