X^2=4x+47

Solution for X^2=4x+47 equation:

X^2=4X+47

We move all terms to the left:

X^2-(4X+47)=0

We get rid of parentheses

X^2-4X-47=0

a = 1; b = -4; c = -47;
Δ = b2-4ac
Δ = -42-4·1·(-47)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{51}}{2*1}=\frac{4-2\sqrt{51}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{51}}{2*1}=\frac{4+2\sqrt{51}}{2}
$