4x^2+24x+13=2x^2+6x

Solution for 4x^2+24x+13=2x^2+6x equation:

4x^2+24x+13=2x^2+6x

We move all terms to the left:

4x^2+24x+13-(2x^2+6x)=0

We get rid of parentheses

4x^2-2x^2+24x-6x+13=0

We add all the numbers together, and all the variables

2x^2+18x+13=0

a = 2; b = 18; c = +13;
Δ = b2-4ac
Δ = 182-4·2·13
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{55}}{2*2}=\frac{-18-2\sqrt{55}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{55}}{2*2}=\frac{-18+2\sqrt{55}}{4}
$