12x(x+5)=13x+2

Solution for 12x(x+5)=13x+2 equation:

12x(x+5)=13x+2

We move all terms to the left:

12x(x+5)-(13x+2)=0

We multiply parentheses

12x^2+60x-(13x+2)=0

We get rid of parentheses

12x^2+60x-13x-2=0

We add all the numbers together, and all the variables

12x^2+47x-2=0

a = 12; b = 47; c = -2;
Δ = b2-4ac
Δ = 472-4·12·(-2)
Δ = 2305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-\sqrt{2305}}{2*12}=\frac{-47-\sqrt{2305}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{2305}}{2*12}=\frac{-47+\sqrt{2305}}{24}
$