4x2+30=182

Solution for 4x2+30=182 equation:

4x^2+30=182

We move all terms to the left:

4x^2+30-(182)=0

We add all the numbers together, and all the variables

4x^2-152=0

a = 4; b = 0; c = -152;
Δ = b2-4ac
Δ = 02-4·4·(-152)
Δ = 2432
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:

$\sqrt{\Delta}=\sqrt{2432}=\sqrt{64*38}=\sqrt{64}*\sqrt{38}=8\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{38}}{2*4}=\frac{0-8\sqrt{38}}{8}
=-\frac{8\sqrt{38}}{8}
=-\sqrt{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{38}}{2*4}=\frac{0+8\sqrt{38}}{8}
=\frac{8\sqrt{38}}{8}
=\sqrt{38}
$