16x-11=(10x-12)(5x+12)

Solution for 16x-11=(10x-12)(5x+12) equation:

16x-11=(10x-12)(5x+12)

We move all terms to the left:

16x-11-((10x-12)(5x+12))=0

We multiply parentheses ..

-((+50x^2+120x-60x-144))+16x-11=0


We calculate terms in parentheses: -((+50x^2+120x-60x-144)), so:

(+50x^2+120x-60x-144)

We get rid of parentheses

50x^2+120x-60x-144

We add all the numbers together, and all the variables

50x^2+60x-144

Back to the equation:

-(50x^2+60x-144)


We add all the numbers together, and all the variables

16x-(50x^2+60x-144)-11=0

We get rid of parentheses

-50x^2+16x-60x+144-11=0

We add all the numbers together, and all the variables

-50x^2-44x+133=0

a = -50; b = -44; c = +133;
Δ = b2-4ac
Δ = -442-4·(-50)·133
Δ = 28536
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:

$\sqrt{\Delta}=\sqrt{28536}=\sqrt{4*7134}=\sqrt{4}*\sqrt{7134}=2\sqrt{7134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{7134}}{2*-50}=\frac{44-2\sqrt{7134}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{7134}}{2*-50}=\frac{44+2\sqrt{7134}}{-100}
$