E=-0.18v^2+1.476v+3.4

Solution for E=-0.18v^2+1.476v+3.4 equation:

=-0.18E^2+1.476E+3.4

We move all terms to the left:

-(-0.18E^2+1.476E+3.4)=0

We get rid of parentheses

0.18E^2-1.476E-3.4=0

a = 0.18; b = -1.476; c = -3.4;
Δ = b2-4ac
Δ = -1.4762-4·0.18·(-3.4)
Δ = 4.626576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.476)-\sqrt{4.626576}}{2*0.18}=\frac{1.476-\sqrt{4.626576}}{0.36}
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.476)+\sqrt{4.626576}}{2*0.18}=\frac{1.476+\sqrt{4.626576}}{0.36}
$