2x+31=3(x2)

Solution for 2x+31=3(x2) equation:

2x+31=3(x2)

We move all terms to the left:

2x+31-(3(x2))=0

determiningTheFunctionDomain
2x-3x2+31=0

We add all the numbers together, and all the variables

-3x^2+2x+31=0

a = -3; b = 2; c = +31;
Δ = b2-4ac
Δ = 22-4·(-3)·31
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{94}}{2*-3}=\frac{-2-2\sqrt{94}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{94}}{2*-3}=\frac{-2+2\sqrt{94}}{-6}
$