5v^2=-7v+34

Solution for 5v^2=-7v+34 equation:

5v^2=-7v+34

We move all terms to the left:

5v^2-(-7v+34)=0

We get rid of parentheses

5v^2+7v-34=0

a = 5; b = 7; c = -34;
Δ = b2-4ac
Δ = 72-4·5·(-34)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-27}{2*5}=\frac{-34}{10}
=-3+2/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+27}{2*5}=\frac{20}{10}
=2
$