91x-8=11+12x(x+5)

Solution for 91x-8=11+12x(x+5) equation:

91x-8=11+12x(x+5)

We move all terms to the left:

91x-8-(11+12x(x+5))=0


We calculate terms in parentheses: -(11+12x(x+5)), so:

11+12x(x+5)

determiningTheFunctionDomain
12x(x+5)+11

We multiply parentheses

12x^2+60x+11

Back to the equation:

-(12x^2+60x+11)


We get rid of parentheses

-12x^2+91x-60x-11-8=0

We add all the numbers together, and all the variables

-12x^2+31x-19=0

a = -12; b = 31; c = -19;
Δ = b2-4ac
Δ = 312-4·(-12)·(-19)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-7}{2*-12}=\frac{-38}{-24}
=1+7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+7}{2*-12}=\frac{-24}{-24}
=1
$