(x-4)(-18)=x(x-14)

Solution for (x-4)(-18)=x(x-14) equation:

(x-4)(-18)=x(x-14)

We move all terms to the left:

(x-4)(-18)-(x(x-14))=0

We multiply parentheses ..

(-18x+72)-(x(x-14))=0


We calculate terms in parentheses: -(x(x-14)), so:

x(x-14)

We multiply parentheses

x^2-14x

Back to the equation:

-(x^2-14x)


We get rid of parentheses

-x^2-18x+14x+72=0

We add all the numbers together, and all the variables

-1x^2-4x+72=0

a = -1; b = -4; c = +72;
Δ = b2-4ac
Δ = -42-4·(-1)·72
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{19}}{2*-1}=\frac{4-4\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{19}}{2*-1}=\frac{4+4\sqrt{19}}{-2}
$