7v^2=2v+22

Solution for 7v^2=2v+22 equation:

7v^2=2v+22

We move all terms to the left:

7v^2-(2v+22)=0

We get rid of parentheses

7v^2-2v-22=0

a = 7; b = -2; c = -22;
Δ = b2-4ac
Δ = -22-4·7·(-22)
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{155}}{2*7}=\frac{2-2\sqrt{155}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{155}}{2*7}=\frac{2+2\sqrt{155}}{14}
$