7v^2-35v-35=7

Solution for 7v^2-35v-35=7 equation:

7v^2-35v-35=7

We move all terms to the left:

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

We add all the numbers together, and all the variables

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