23=3x^2+7

Solution for 23=3x^2+7 equation:

23=3x^2+7

We move all terms to the left:

23-(3x^2+7)=0

We get rid of parentheses

-3x^2-7+23=0

We add all the numbers together, and all the variables

-3x^2+16=0

a = -3; b = 0; c = +16;
Δ = b2-4ac
Δ = 02-4·(-3)·16
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-3}=\frac{0-8\sqrt{3}}{-6}
=-\frac{8\sqrt{3}}{-6}
=-\frac{4\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-3}=\frac{0+8\sqrt{3}}{-6}
=\frac{8\sqrt{3}}{-6}
=\frac{4\sqrt{3}}{-3}
$