3v^2+87v=-4v^2+3v-224

Solution for 3v^2+87v=-4v^2+3v-224 equation:

3v^2+87v=-4v^2+3v-224

We move all terms to the left:

3v^2+87v-(-4v^2+3v-224)=0

We get rid of parentheses

3v^2+4v^2-3v+87v+224=0

We add all the numbers together, and all the variables

7v^2+84v+224=0

a = 7; b = 84; c = +224;
Δ = b2-4ac
Δ = 842-4·7·224
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-28}{2*7}=\frac{-112}{14}
=-8
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+28}{2*7}=\frac{-56}{14}
=-4
$