(6x-4=13x-67)X=

Solution for (6x-4=13x-67)X= equation:

(6x-4=13x-67)x=

We move all terms to the left:

(6x-4-(13x-67)x)=0


We calculate terms in parentheses: +(6x-4-(13x-67)x), so:

6x-4-(13x-67)x

determiningTheFunctionDomain
6x-(13x-67)x-4

We multiply parentheses

-13x^2+6x+67x-4

We add all the numbers together, and all the variables

-13x^2+73x-4

Back to the equation:

+(-13x^2+73x-4)


We get rid of parentheses

-13x^2+73x-4=0

a = -13; b = 73; c = -4;
Δ = b2-4ac
Δ = 732-4·(-13)·(-4)
Δ = 5121
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:

$\sqrt{\Delta}=\sqrt{5121}=\sqrt{9*569}=\sqrt{9}*\sqrt{569}=3\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(73)-3\sqrt{569}}{2*-13}=\frac{-73-3\sqrt{569}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(73)+3\sqrt{569}}{2*-13}=\frac{-73+3\sqrt{569}}{-26}
$