4v2+7v-22=-7

Solution for 4v2+7v-22=-7 equation:

4v^2+7v-22=-7

We move all terms to the left:

4v^2+7v-22-(-7)=0

We add all the numbers together, and all the variables

4v^2+7v-15=0

a = 4; b = 7; c = -15;
Δ = b2-4ac
Δ = 72-4·4·(-15)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*4}=\frac{-24}{8}
=-3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*4}=\frac{10}{8}
=1+1/4
$