3x^2+22=374

Solution for 3x^2+22=374 equation:

3x^2+22=374

We move all terms to the left:

3x^2+22-(374)=0

We add all the numbers together, and all the variables

3x^2-352=0

a = 3; b = 0; c = -352;
Δ = b2-4ac
Δ = 02-4·3·(-352)
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*3}=\frac{0-8\sqrt{66}}{6}
=-\frac{8\sqrt{66}}{6}
=-\frac{4\sqrt{66}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*3}=\frac{0+8\sqrt{66}}{6}
=\frac{8\sqrt{66}}{6}
=\frac{4\sqrt{66}}{3}
$