7v^2+47v+38=8

Solution for 7v^2+47v+38=8 equation:

7v^2+47v+38=8

We move all terms to the left:

7v^2+47v+38-(8)=0

We add all the numbers together, and all the variables

7v^2+47v+30=0

a = 7; b = 47; c = +30;
Δ = b2-4ac
Δ = 472-4·7·30
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-37}{2*7}=\frac{-84}{14}
=-6
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+37}{2*7}=\frac{-10}{14}
=-5/7
$