5v2+12v=13

Solution for 5v2+12v=13 equation:

5v^2+12v=13

We move all terms to the left:

5v^2+12v-(13)=0

a = 5; b = 12; c = -13;
Δ = b2-4ac
Δ = 122-4·5·(-13)
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{101}}{2*5}=\frac{-12-2\sqrt{101}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{101}}{2*5}=\frac{-12+2\sqrt{101}}{10}
$