7x^2-53x=24

Solution for 7x^2-53x=24 equation:

7x^2-53x=24

We move all terms to the left:

7x^2-53x-(24)=0

a = 7; b = -53; c = -24;
Δ = b2-4ac
Δ = -532-4·7·(-24)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-59}{2*7}=\frac{-6}{14}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+59}{2*7}=\frac{112}{14}
=8
$