8x^2-7=24x-0

Solution for 8x^2-7=24x-0 equation:

8x^2-7=24x-0

We move all terms to the left:

8x^2-7-(24x-0)=0

We add all the numbers together, and all the variables

8x^2-(+24x)-7=0

We get rid of parentheses

8x^2-24x-7=0

a = 8; b = -24; c = -7;
Δ = b2-4ac
Δ = -242-4·8·(-7)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20\sqrt{2}}{2*8}=\frac{24-20\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20\sqrt{2}}{2*8}=\frac{24+20\sqrt{2}}{16}
$