(x+10)(x+3)=60

Solution for (x+10)(x+3)=60 equation:

(x+10)(x+3)=60

We move all terms to the left:

(x+10)(x+3)-(60)=0

We multiply parentheses ..

(+x^2+3x+10x+30)-60=0

We get rid of parentheses

x^2+3x+10x+30-60=0

We add all the numbers together, and all the variables

x^2+13x-30=0

a = 1; b = 13; c = -30;
Δ = b2-4ac
Δ = 132-4·1·(-30)
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{-(13)-17}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*1}=\frac{4}{2}
=2
$