X^2-7x=24

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

X^2-7X=24

We move all terms to the left:

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

a = 1; b = -7; c = -24;
Δ = b2-4ac
Δ = -72-4·1·(-24)
Δ = 145
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{-(-7)-\sqrt{145}}{2*1}=\frac{7-\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*1}=\frac{7+\sqrt{145}}{2}
$