5v^2-38v+46=-2

Solution for 5v^2-38v+46=-2 equation:

5v^2-38v+46=-2

We move all terms to the left:

5v^2-38v+46-(-2)=0

We add all the numbers together, and all the variables

5v^2-38v+48=0

a = 5; b = -38; c = +48;
Δ = b2-4ac
Δ = -382-4·5·48
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22}{2*5}=\frac{16}{10}
=1+3/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22}{2*5}=\frac{60}{10}
=6
$