X(x-4)=4x+49

Solution for X(x-4)=4x+49 equation:

X(X-4)=4X+49

We move all terms to the left:

X(X-4)-(4X+49)=0

We multiply parentheses

X^2-4X-(4X+49)=0

We get rid of parentheses

X^2-4X-4X-49=0

We add all the numbers together, and all the variables

X^2-8X-49=0

a = 1; b = -8; c = -49;
Δ = b2-4ac
Δ = -82-4·1·(-49)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{65}}{2*1}=\frac{8-2\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{65}}{2*1}=\frac{8+2\sqrt{65}}{2}
$