7=(x)(6x-1)

Solution for 7=(x)(6x-1) equation:

7=(x)(6x-1)

We move all terms to the left:

7-((x)(6x-1))=0


We calculate terms in parentheses: -(x(6x-1)), so:

x(6x-1)

We multiply parentheses

6x^2-1x

Back to the equation:

-(6x^2-1x)


We get rid of parentheses

-6x^2+1x+7=0

We add all the numbers together, and all the variables

-6x^2+x+7=0

a = -6; b = 1; c = +7;
Δ = b2-4ac
Δ = 12-4·(-6)·7
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*-6}=\frac{-14}{-12}
=1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*-6}=\frac{12}{-12}
=-1
$