(x*x)+(12*x)=144

Solution for (x*x)+(12*x)=144 equation:

(x*x)+(12x)=144

We move all terms to the left:

(x*x)+(12x)-(144)=0

We add all the numbers together, and all the variables

(+x*x)+12x-144=0

We add all the numbers together, and all the variables

12x+(+x*x)-144=0

We get rid of parentheses

12x+x*x-144=0

Wy multiply elements

x^2+12x-144=0

a = 1; b = 12; c = -144;
Δ = b2-4ac
Δ = 122-4·1·(-144)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{5}}{2*1}=\frac{-12-12\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{5}}{2*1}=\frac{-12+12\sqrt{5}}{2}
$