x(x+12)=14(x+18)

Solution for x(x+12)=14(x+18) equation:

x(x+12)=14(x+18)

We move all terms to the left:

x(x+12)-(14(x+18))=0

We multiply parentheses

x^2+12x-(14(x+18))=0


We calculate terms in parentheses: -(14(x+18)), so:

14(x+18)

We multiply parentheses

14x+252

Back to the equation:

-(14x+252)


We get rid of parentheses

x^2+12x-14x-252=0

We add all the numbers together, and all the variables

x^2-2x-252=0

a = 1; b = -2; c = -252;
Δ = b2-4ac
Δ = -22-4·1·(-252)
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{253}}{2*1}=\frac{2-2\sqrt{253}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{253}}{2*1}=\frac{2+2\sqrt{253}}{2}
$