4v^2-5v-17=7

Solution for 4v^2-5v-17=7 equation:

4v^2-5v-17=7

We move all terms to the left:

4v^2-5v-17-(7)=0

We add all the numbers together, and all the variables

4v^2-5v-24=0

a = 4; b = -5; c = -24;
Δ = b2-4ac
Δ = -52-4·4·(-24)
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{409}}{2*4}=\frac{5-\sqrt{409}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{409}}{2*4}=\frac{5+\sqrt{409}}{8}
$