8v(3v-11)=70

Solution for 8v(3v-11)=70 equation:

8v(3v-11)=70

We move all terms to the left:

8v(3v-11)-(70)=0

We multiply parentheses

24v^2-88v-70=0

a = 24; b = -88; c = -70;
Δ = b2-4ac
Δ = -882-4·24·(-70)
Δ = 14464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14464}=\sqrt{64*226}=\sqrt{64}*\sqrt{226}=8\sqrt{226}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{226}}{2*24}=\frac{88-8\sqrt{226}}{48}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{226}}{2*24}=\frac{88+8\sqrt{226}}{48}
$