8x^2-22=74

Solution for 8x^2-22=74 equation:

8x^2-22=74

We move all terms to the left:

8x^2-22-(74)=0

We add all the numbers together, and all the variables

8x^2-96=0

a = 8; b = 0; c = -96;
Δ = b2-4ac
Δ = 02-4·8·(-96)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*8}=\frac{0-32\sqrt{3}}{16}
=-\frac{32\sqrt{3}}{16}
=-2\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*8}=\frac{0+32\sqrt{3}}{16}
=\frac{32\sqrt{3}}{16}
=2\sqrt{3}
$