2x+5=3x2+2x-7

Solution for 2x+5=3x2+2x-7 equation:

2x+5=3x^2+2x-7

We move all terms to the left:

2x+5-(3x^2+2x-7)=0

We get rid of parentheses

-3x^2+2x-2x+7+5=0

We add all the numbers together, and all the variables

-3x^2+12=0

a = -3; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-3)·12
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-3}=\frac{12}{-6}
=-2
$