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

Solution for 0=(7-x)(6x+1) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((-6x^2-1x+42x+7))=0


We calculate terms in parentheses: -((-6x^2-1x+42x+7)), so:

(-6x^2-1x+42x+7)

We get rid of parentheses

-6x^2-1x+42x+7

We add all the numbers together, and all the variables

-6x^2+41x+7

Back to the equation:

-(-6x^2+41x+7)


We get rid of parentheses

6x^2-41x-7=0

a = 6; b = -41; c = -7;
Δ = b2-4ac
Δ = -412-4·6·(-7)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-43}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+43}{2*6}=\frac{84}{12}
=7
$