3x+2x^2-8=67

Solution for 3x+2x^2-8=67 equation:

3x+2x^2-8=67

We move all terms to the left:

3x+2x^2-8-(67)=0

We add all the numbers together, and all the variables

2x^2+3x-75=0

a = 2; b = 3; c = -75;
Δ = b2-4ac
Δ = 32-4·2·(-75)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{609}}{2*2}=\frac{-3-\sqrt{609}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{609}}{2*2}=\frac{-3+\sqrt{609}}{4}
$