x(x-14)=2(x+13)

Solution for x(x-14)=2(x+13) equation:

x(x-14)=2(x+13)

We move all terms to the left:

x(x-14)-(2(x+13))=0

We multiply parentheses

x^2-14x-(2(x+13))=0


We calculate terms in parentheses: -(2(x+13)), so:

2(x+13)

We multiply parentheses

2x+26

Back to the equation:

-(2x+26)


We get rid of parentheses

x^2-14x-2x-26=0

We add all the numbers together, and all the variables

x^2-16x-26=0

a = 1; b = -16; c = -26;
Δ = b2-4ac
Δ = -162-4·1·(-26)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{10}}{2*1}=\frac{16-6\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{10}}{2*1}=\frac{16+6\sqrt{10}}{2}
$