v^2-4v=43

Solution for v^2-4v=43 equation:

v^2-4v=43

We move all terms to the left:

v^2-4v-(43)=0

a = 1; b = -4; c = -43;
Δ = b2-4ac
Δ = -42-4·1·(-43)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{47}}{2*1}=\frac{4-2\sqrt{47}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{47}}{2*1}=\frac{4+2\sqrt{47}}{2}
$