7x^2-2-6x=0

Solution for 7x^2-2-6x=0 equation:

7x^2-2-6x=0

a = 7; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·7·(-2)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{23}}{2*7}=\frac{6-2\sqrt{23}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{23}}{2*7}=\frac{6+2\sqrt{23}}{14}
$