X(x-3)-51=3x+13

Solution for X(x-3)-51=3x+13 equation:

X(X-3)-51=3X+13

We move all terms to the left:

X(X-3)-51-(3X+13)=0

We multiply parentheses

X^2-3X-(3X+13)-51=0

We get rid of parentheses

X^2-3X-3X-13-51=0

We add all the numbers together, and all the variables

X^2-6X-64=0

a = 1; b = -6; c = -64;
Δ = b2-4ac
Δ = -62-4·1·(-64)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{73}}{2*1}=\frac{6-2\sqrt{73}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{73}}{2*1}=\frac{6+2\sqrt{73}}{2}
$