5e+2e^2=150

Solution for 5e+2e^2=150 equation:

5e+2e^2=150

We move all terms to the left:

5e+2e^2-(150)=0

a = 2; b = 5; c = -150;
Δ = b2-4ac
Δ = 52-4·2·(-150)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*2}=\frac{-40}{4}
=-10
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*2}=\frac{30}{4}
=7+1/2
$