X2+4=40-6x

Solution for X2+4=40-6x equation:

X2+4=40-6X

We move all terms to the left:

X2+4-(40-6X)=0

We add all the numbers together, and all the variables

X2-(-6X+40)+4=0

We add all the numbers together, and all the variables

X^2-(-6X+40)+4=0

We get rid of parentheses

X^2+6X-40+4=0

We add all the numbers together, and all the variables

X^2+6X-36=0

a = 1; b = 6; c = -36;
Δ = b2-4ac
Δ = 62-4·1·(-36)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*1}=\frac{-6-6\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*1}=\frac{-6+6\sqrt{5}}{2}
$