60+7x=x^2

Solution for 60+7x=x^2 equation:

60+7x=x^2

We move all terms to the left:

60+7x-(x^2)=0

determiningTheFunctionDomain
-x^2+7x+60=0

We add all the numbers together, and all the variables

-1x^2+7x+60=0

a = -1; b = 7; c = +60;
Δ = b2-4ac
Δ = 72-4·(-1)·60
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*-1}=\frac{10}{-2}
=-5
$