3e^2-5e=3

Solution for 3e^2-5e=3 equation:

3e^2-5e=3

We move all terms to the left:

3e^2-5e-(3)=0

a = 3; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·3·(-3)
Δ = 61
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{-(-5)-\sqrt{61}}{2*3}=\frac{5-\sqrt{61}}{6}
$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{61}}{2*3}=\frac{5+\sqrt{61}}{6}
$