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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+10x-12=0

a = 3; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·3·(-12)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{61}}{2*3}=\frac{-10-2\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{61}}{2*3}=\frac{-10+2\sqrt{61}}{6}
$