3x^2-7=40

Solution for 3x^2-7=40 equation:

3x^2-7=40

We move all terms to the left:

3x^2-7-(40)=0

We add all the numbers together, and all the variables

3x^2-47=0

a = 3; b = 0; c = -47;
Δ = b2-4ac
Δ = 02-4·3·(-47)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{141}}{2*3}=\frac{0-2\sqrt{141}}{6}
=-\frac{2\sqrt{141}}{6}
=-\frac{\sqrt{141}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{141}}{2*3}=\frac{0+2\sqrt{141}}{6}
=\frac{2\sqrt{141}}{6}
=\frac{\sqrt{141}}{3}
$