(v+7)(v+7)=2v^2-18v+44

Solution for (v+7)(v+7)=2v^2-18v+44 equation:

(v+7)(v+7)=2v^2-18v+44

We move all terms to the left:

(v+7)(v+7)-(2v^2-18v+44)=0

We get rid of parentheses

-2v^2+(v+7)(v+7)+18v-44=0

We multiply parentheses ..

-2v^2+(+v^2+7v+7v+49)+18v-44=0

We get rid of parentheses

-2v^2+v^2+7v+7v+18v+49-44=0

We add all the numbers together, and all the variables

-1v^2+32v+5=0

a = -1; b = 32; c = +5;
Δ = b2-4ac
Δ = 322-4·(-1)·5
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-6\sqrt{29}}{2*-1}=\frac{-32-6\sqrt{29}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+6\sqrt{29}}{2*-1}=\frac{-32+6\sqrt{29}}{-2}
$