(9v+6)(7v+4)=90

Solution for (9v+6)(7v+4)=90 equation:

(9v+6)(7v+4)=90

We move all terms to the left:

(9v+6)(7v+4)-(90)=0

We multiply parentheses ..

(+63v^2+36v+42v+24)-90=0

We get rid of parentheses

63v^2+36v+42v+24-90=0

We add all the numbers together, and all the variables

63v^2+78v-66=0

a = 63; b = 78; c = -66;
Δ = b2-4ac
Δ = 782-4·63·(-66)
Δ = 22716
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:

$\sqrt{\Delta}=\sqrt{22716}=\sqrt{36*631}=\sqrt{36}*\sqrt{631}=6\sqrt{631}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{631}}{2*63}=\frac{-78-6\sqrt{631}}{126}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{631}}{2*63}=\frac{-78+6\sqrt{631}}{126}
$