2v^2+74=4-24v

Solution for 2v^2+74=4-24v equation:

2v^2+74=4-24v

We move all terms to the left:

2v^2+74-(4-24v)=0

We add all the numbers together, and all the variables

2v^2-(-24v+4)+74=0

We get rid of parentheses

2v^2+24v-4+74=0

We add all the numbers together, and all the variables

2v^2+24v+70=0

a = 2; b = 24; c = +70;
Δ = b2-4ac
Δ = 242-4·2·70
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4}{2*2}=\frac{-28}{4}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4}{2*2}=\frac{-20}{4}
=-5
$