7v2-42=-35v

Solution for 7v2-42=-35v equation:

7v^2-42=-35v

We move all terms to the left:

7v^2-42-(-35v)=0

We get rid of parentheses

7v^2+35v-42=0

a = 7; b = 35; c = -42;
Δ = b2-4ac
Δ = 352-4·7·(-42)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-49}{2*7}=\frac{-84}{14}
=-6
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+49}{2*7}=\frac{14}{14}
=1
$