X^2-6x=7x+24

Solution for X^2-6x=7x+24 equation:

X^2-6X=7X+24

We move all terms to the left:

X^2-6X-(7X+24)=0

We get rid of parentheses

X^2-6X-7X-24=0

We add all the numbers together, and all the variables

X^2-13X-24=0

a = 1; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·1·(-24)
Δ = 265
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{-(-13)-\sqrt{265}}{2*1}=\frac{13-\sqrt{265}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{265}}{2*1}=\frac{13+\sqrt{265}}{2}
$