X^2-8x=17x+24

Solution for X^2-8x=17x+24 equation:

X^2-8X=17X+24

We move all terms to the left:

X^2-8X-(17X+24)=0

We get rid of parentheses

X^2-8X-17X-24=0

We add all the numbers together, and all the variables

X^2-25X-24=0

a = 1; b = -25; c = -24;
Δ = b2-4ac
Δ = -252-4·1·(-24)
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{721}}{2*1}=\frac{25-\sqrt{721}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{721}}{2*1}=\frac{25+\sqrt{721}}{2}
$