(6+x)*x=(7+5)*5

Solution for (6+x)*x=(7+5)*5 equation:

(6+x)*x=(7+5)*5

We move all terms to the left:

(6+x)*x-((7+5)*5)=0

We add all the numbers together, and all the variables

(x+6)*x-(12*5)=0

We add all the numbers together, and all the variables

(x+6)*x-60=0

We multiply parentheses

x^2+6x-60=0

a = 1; b = 6; c = -60;
Δ = b2-4ac
Δ = 62-4·1·(-60)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*1}=\frac{-6-2\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*1}=\frac{-6+2\sqrt{69}}{2}
$