7x^2=6x-1

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

7x^2=6x-1

We move all terms to the left:

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

We get rid of parentheses

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}
$