7x^2-23-6=0

Solution for 7x^2-23-6=0 equation:

7x^2-23-6=0

We add all the numbers together, and all the variables

7x^2-29=0

a = 7; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·7·(-29)
Δ = 812
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:

$\sqrt{\Delta}=\sqrt{812}=\sqrt{4*203}=\sqrt{4}*\sqrt{203}=2\sqrt{203}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{203}}{2*7}=\frac{0-2\sqrt{203}}{14}
=-\frac{2\sqrt{203}}{14}
=-\frac{\sqrt{203}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{203}}{2*7}=\frac{0+2\sqrt{203}}{14}
=\frac{2\sqrt{203}}{14}
=\frac{\sqrt{203}}{7}
$