7x2-100=24

Solution for 7x2-100=24 equation:

7x^2-100=24

We move all terms to the left:

7x^2-100-(24)=0

We add all the numbers together, and all the variables

7x^2-124=0

a = 7; b = 0; c = -124;
Δ = b2-4ac
Δ = 02-4·7·(-124)
Δ = 3472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3472}=\sqrt{16*217}=\sqrt{16}*\sqrt{217}=4\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{217}}{2*7}=\frac{0-4\sqrt{217}}{14}
=-\frac{4\sqrt{217}}{14}
=-\frac{2\sqrt{217}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{217}}{2*7}=\frac{0+4\sqrt{217}}{14}
=\frac{4\sqrt{217}}{14}
=\frac{2\sqrt{217}}{7}
$