7v^2+40v=-25

Solution for 7v^2+40v=-25 equation:

7v^2+40v=-25

We move all terms to the left:

7v^2+40v-(-25)=0

We add all the numbers together, and all the variables

7v^2+40v+25=0

a = 7; b = 40; c = +25;
Δ = b2-4ac
Δ = 402-4·7·25
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-30}{2*7}=\frac{-70}{14}
=-5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+30}{2*7}=\frac{-10}{14}
=-5/7
$