3x+2x^2=77

Solution for 3x+2x^2=77 equation:

3x+2x^2=77

We move all terms to the left:

3x+2x^2-(77)=0

a = 2; b = 3; c = -77;
Δ = b2-4ac
Δ = 32-4·2·(-77)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-25}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+25}{2*2}=\frac{22}{4}
=5+1/2
$