12x(13x-19)-(11x-15)=25-(17-13x)

Solution for 12x(13x-19)-(11x-15)=25-(17-13x) equation:

12x(13x-19)-(11x-15)=25-(17-13x)

We move all terms to the left:

12x(13x-19)-(11x-15)-(25-(17-13x))=0

We add all the numbers together, and all the variables

12x(13x-19)-(11x-15)-(25-(-13x+17))=0

We multiply parentheses

156x^2-228x-(11x-15)-(25-(-13x+17))=0

We get rid of parentheses

156x^2-228x-11x-(25-(-13x+17))+15=0


We calculate terms in parentheses: -(25-(-13x+17)), so:

25-(-13x+17)

determiningTheFunctionDomain
-(-13x+17)+25

We get rid of parentheses

13x-17+25

We add all the numbers together, and all the variables

13x+8

Back to the equation:

-(13x+8)


We add all the numbers together, and all the variables

156x^2-239x-(13x+8)+15=0

We get rid of parentheses

156x^2-239x-13x-8+15=0

We add all the numbers together, and all the variables

156x^2-252x+7=0

a = 156; b = -252; c = +7;
Δ = b2-4ac
Δ = -2522-4·156·7
Δ = 59136
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:

$\sqrt{\Delta}=\sqrt{59136}=\sqrt{256*231}=\sqrt{256}*\sqrt{231}=16\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-16\sqrt{231}}{2*156}=\frac{252-16\sqrt{231}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+16\sqrt{231}}{2*156}=\frac{252+16\sqrt{231}}{312}
$