2x+8x+36=2x^2+14x+24

Solution for 2x+8x+36=2x^2+14x+24 equation:

2x+8x+36=2x^2+14x+24

We move all terms to the left:

2x+8x+36-(2x^2+14x+24)=0

We add all the numbers together, and all the variables

10x-(2x^2+14x+24)+36=0

We get rid of parentheses

-2x^2+10x-14x-24+36=0

We add all the numbers together, and all the variables

-2x^2-4x+12=0

a = -2; b = -4; c = +12;
Δ = b2-4ac
Δ = -42-4·(-2)·12
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*-2}=\frac{4-4\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*-2}=\frac{4+4\sqrt{7}}{-4}
$