7v(v-2)=-6v+25

Solution for 7v(v-2)=-6v+25 equation:

7v(v-2)=-6v+25

We move all terms to the left:

7v(v-2)-(-6v+25)=0

We multiply parentheses

7v^2-14v-(-6v+25)=0

We get rid of parentheses

7v^2-14v+6v-25=0

We add all the numbers together, and all the variables

7v^2-8v-25=0

a = 7; b = -8; c = -25;
Δ = b2-4ac
Δ = -82-4·7·(-25)
Δ = 764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{764}=\sqrt{4*191}=\sqrt{4}*\sqrt{191}=2\sqrt{191}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{191}}{2*7}=\frac{8-2\sqrt{191}}{14}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{191}}{2*7}=\frac{8+2\sqrt{191}}{14}
$