24=X2+6x+8/2

Solution for 24=X2+6x+8/2 equation:

24=X2+6X+8/2

We move all terms to the left:

24-(X2+6X+8/2)=0

We add all the numbers together, and all the variables

-(+X^2+6X+8/2)+24=0

We get rid of parentheses

-X^2-6X+24-8/2=0

We multiply all the terms by the denominator


-X^2*2-6X*2-8+24*2=0

We add all the numbers together, and all the variables

-X^2*2-6X*2+40=0

Wy multiply elements

-2X^2-12X+40=0

a = -2; b = -12; c = +40;
Δ = b2-4ac
Δ = -122-4·(-2)·40
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{29}}{2*-2}=\frac{12-4\sqrt{29}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{29}}{2*-2}=\frac{12+4\sqrt{29}}{-4}
$