6x-1=7x^2

Solution for 6x-1=7x^2 equation:

6x-1=7x^2

We move all terms to the left:

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

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

a = -7; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·(-7)·(-1)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2}}{2*-7}=\frac{-6-2\sqrt{2}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2}}{2*-7}=\frac{-6+2\sqrt{2}}{-14}
$