(v+5)2+30+v2=380

Solution for (v+5)2+30+v2=380 equation:

(v+5)2+30+v2=380

We move all terms to the left:

(v+5)2+30+v2-(380)=0

We add all the numbers together, and all the variables

v^2+(v+5)2-350=0

We multiply parentheses

v^2+2v+10-350=0

We add all the numbers together, and all the variables

v^2+2v-340=0

a = 1; b = 2; c = -340;
Δ = b2-4ac
Δ = 22-4·1·(-340)
Δ = 1364
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:

$\sqrt{\Delta}=\sqrt{1364}=\sqrt{4*341}=\sqrt{4}*\sqrt{341}=2\sqrt{341}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{341}}{2*1}=\frac{-2-2\sqrt{341}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{341}}{2*1}=\frac{-2+2\sqrt{341}}{2}
$