(3x^2+12x+13)=2x+5

Solution for (3x^2+12x+13)=2x+5 equation:

(3x^2+12x+13)=2x+5

We move all terms to the left:

(3x^2+12x+13)-(2x+5)=0

We get rid of parentheses

3x^2+12x-2x+13-5=0

We add all the numbers together, and all the variables

3x^2+10x+8=0

a = 3; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·3·8
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*3}=\frac{-8}{6}
=-1+1/3
$