X2+4x=27

Solution for X2+4x=27 equation:

X2+4X=27

We move all terms to the left:

X2+4X-(27)=0

We add all the numbers together, and all the variables

X^2+4X-27=0

a = 1; b = 4; c = -27;
Δ = b2-4ac
Δ = 42-4·1·(-27)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{31}}{2*1}=\frac{-4-2\sqrt{31}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{31}}{2*1}=\frac{-4+2\sqrt{31}}{2}
$