3v^2+7v=4

Solution for 3v^2+7v=4 equation:

3v^2+7v=4

We move all terms to the left:

3v^2+7v-(4)=0

a = 3; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·3·(-4)
Δ = 97
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{-(7)-\sqrt{97}}{2*3}=\frac{-7-\sqrt{97}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*3}=\frac{-7+\sqrt{97}}{6}
$