4x2+72=230

Solution for 4x2+72=230 equation:

4x^2+72=230

We move all terms to the left:

4x^2+72-(230)=0

We add all the numbers together, and all the variables

4x^2-158=0

a = 4; b = 0; c = -158;
Δ = b2-4ac
Δ = 02-4·4·(-158)
Δ = 2528
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:

$\sqrt{\Delta}=\sqrt{2528}=\sqrt{16*158}=\sqrt{16}*\sqrt{158}=4\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{158}}{2*4}=\frac{0-4\sqrt{158}}{8}
=-\frac{4\sqrt{158}}{8}
=-\frac{\sqrt{158}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{158}}{2*4}=\frac{0+4\sqrt{158}}{8}
=\frac{4\sqrt{158}}{8}
=\frac{\sqrt{158}}{2}
$