12x(x-5)=11(x+5)

Solution for 12x(x-5)=11(x+5) equation:

12x(x-5)=11(x+5)

We move all terms to the left:

12x(x-5)-(11(x+5))=0

We multiply parentheses

12x^2-60x-(11(x+5))=0


We calculate terms in parentheses: -(11(x+5)), so:

11(x+5)

We multiply parentheses

11x+55

Back to the equation:

-(11x+55)


We get rid of parentheses

12x^2-60x-11x-55=0

We add all the numbers together, and all the variables

12x^2-71x-55=0

a = 12; b = -71; c = -55;
Δ = b2-4ac
Δ = -712-4·12·(-55)
Δ = 7681
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{-(-71)-\sqrt{7681}}{2*12}=\frac{71-\sqrt{7681}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{7681}}{2*12}=\frac{71+\sqrt{7681}}{24}
$