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

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

X=(7X-1)(6X-1)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

42X^2-13X+1

Back to the equation:

-(42X^2-13X+1)


We add all the numbers together, and all the variables

X-(42X^2-13X+1)=0

We get rid of parentheses

-42X^2+X+13X-1=0

We add all the numbers together, and all the variables

-42X^2+14X-1=0

a = -42; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·(-42)·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{7}}{2*-42}=\frac{-14-2\sqrt{7}}{-84}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{7}}{2*-42}=\frac{-14+2\sqrt{7}}{-84}
$