3x+2x^2=72

Solution for 3x+2x^2=72 equation:

3x+2x^2=72

We move all terms to the left:

3x+2x^2-(72)=0

a = 2; b = 3; c = -72;
Δ = b2-4ac
Δ = 32-4·2·(-72)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{65}}{2*2}=\frac{-3-3\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{65}}{2*2}=\frac{-3+3\sqrt{65}}{4}
$