x=(12x+3)(7x-13)

Solution for x=(12x+3)(7x-13) equation:

x=(12x+3)(7x-13)

We move all terms to the left:

x-((12x+3)(7x-13))=0

We multiply parentheses ..

-((+84x^2-156x+21x-39))+x=0


We calculate terms in parentheses: -((+84x^2-156x+21x-39)), so:

(+84x^2-156x+21x-39)

We get rid of parentheses

84x^2-156x+21x-39

We add all the numbers together, and all the variables

84x^2-135x-39

Back to the equation:

-(84x^2-135x-39)


We add all the numbers together, and all the variables

x-(84x^2-135x-39)=0

We get rid of parentheses

-84x^2+x+135x+39=0

We add all the numbers together, and all the variables

-84x^2+136x+39=0

a = -84; b = 136; c = +39;
Δ = b2-4ac
Δ = 1362-4·(-84)·39
Δ = 31600
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:

$\sqrt{\Delta}=\sqrt{31600}=\sqrt{400*79}=\sqrt{400}*\sqrt{79}=20\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-20\sqrt{79}}{2*-84}=\frac{-136-20\sqrt{79}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+20\sqrt{79}}{2*-84}=\frac{-136+20\sqrt{79}}{-168}
$