8s^2-68-38=0

Solution for 8s^2-68-38=0 equation:

8s^2-68-38=0

We add all the numbers together, and all the variables

8s^2-106=0

a = 8; b = 0; c = -106;
Δ = b2-4ac
Δ = 02-4·8·(-106)
Δ = 3392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3392}=\sqrt{64*53}=\sqrt{64}*\sqrt{53}=8\sqrt{53}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{53}}{2*8}=\frac{0-8\sqrt{53}}{16}
=-\frac{8\sqrt{53}}{16}
=-\frac{\sqrt{53}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{53}}{2*8}=\frac{0+8\sqrt{53}}{16}
=\frac{8\sqrt{53}}{16}
=\frac{\sqrt{53}}{2}
$