10*6=(12+x)*x

Solution for 10*6=(12+x)*x equation:

10*6=(12+x)*x

We move all terms to the left:

10*6-((12+x)*x)=0

We add all the numbers together, and all the variables

-((x+12)*x)+10*6=0

We add all the numbers together, and all the variables

-((x+12)*x)+60=0


We calculate terms in parentheses: -((x+12)*x), so:

(x+12)*x

We multiply parentheses

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x+60=0

We add all the numbers together, and all the variables

-1x^2-12x+60=0

a = -1; b = -12; c = +60;
Δ = b2-4ac
Δ = -122-4·(-1)·60
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*-1}=\frac{12-8\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*-1}=\frac{12+8\sqrt{6}}{-2}
$