74=3x^2+10

Solution for 74=3x^2+10 equation:

74=3x^2+10

We move all terms to the left:

74-(3x^2+10)=0

We get rid of parentheses

-3x^2-10+74=0

We add all the numbers together, and all the variables

-3x^2+64=0

a = -3; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-3)·64
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-3}=\frac{0-16\sqrt{3}}{-6}
=-\frac{16\sqrt{3}}{-6}
=-\frac{8\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-3}=\frac{0+16\sqrt{3}}{-6}
=\frac{16\sqrt{3}}{-6}
=\frac{8\sqrt{3}}{-3}
$