x=(13X+3)*(6x-1)

Solution for x=(13X+3)*(6x-1) equation:

x=(13x+3)(6x-1)

We move all terms to the left:

x-((13x+3)(6x-1))=0

We multiply parentheses ..

-((+78x^2-13x+18x-3))+x=0


We calculate terms in parentheses: -((+78x^2-13x+18x-3)), so:

(+78x^2-13x+18x-3)

We get rid of parentheses

78x^2-13x+18x-3

We add all the numbers together, and all the variables

78x^2+5x-3

Back to the equation:

-(78x^2+5x-3)


We add all the numbers together, and all the variables

x-(78x^2+5x-3)=0

We get rid of parentheses

-78x^2+x-5x+3=0

We add all the numbers together, and all the variables

-78x^2-4x+3=0

a = -78; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-78)·3
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{238}}{2*-78}=\frac{4-2\sqrt{238}}{-156}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{238}}{2*-78}=\frac{4+2\sqrt{238}}{-156}
$