x^2-(x^2)/4=148

Solution for x^2-(x^2)/4=148 equation:

x^2-(x^2)/4=148

We move all terms to the left:

x^2-(x^2)/4-(148)=0

We multiply all the terms by the denominator


-x^2+x^2*4-148*4=0

We add all the numbers together, and all the variables

-1x^2+x^2*4-592=0

Wy multiply elements

-1x^2+4x^2-592=0

We add all the numbers together, and all the variables

3x^2-592=0

a = 3; b = 0; c = -592;
Δ = b2-4ac
Δ = 02-4·3·(-592)
Δ = 7104
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:

$\sqrt{\Delta}=\sqrt{7104}=\sqrt{64*111}=\sqrt{64}*\sqrt{111}=8\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{111}}{2*3}=\frac{0-8\sqrt{111}}{6}
=-\frac{8\sqrt{111}}{6}
=-\frac{4\sqrt{111}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{111}}{2*3}=\frac{0+8\sqrt{111}}{6}
=\frac{8\sqrt{111}}{6}
=\frac{4\sqrt{111}}{3}
$