2x+5=3x^2+2x-12

Solution for 2x+5=3x^2+2x-12 equation:

2x+5=3x^2+2x-12

We move all terms to the left:

2x+5-(3x^2+2x-12)=0

We get rid of parentheses

-3x^2+2x-2x+12+5=0

We add all the numbers together, and all the variables

-3x^2+17=0

a = -3; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-3)·17
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*-3}=\frac{0-2\sqrt{51}}{-6}
=-\frac{2\sqrt{51}}{-6}
=-\frac{\sqrt{51}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*-3}=\frac{0+2\sqrt{51}}{-6}
=\frac{2\sqrt{51}}{-6}
=\frac{\sqrt{51}}{-3}
$