75=1/2x2

Solution for 75=1/2x2 equation:

75=1/2x^2

We move all terms to the left:

75-(1/2x^2)=0


Domain of the equation: 2x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/2x^2+75=0

We multiply all the terms by the denominator


75*2x^2-1=0

Wy multiply elements

150x^2-1=0

a = 150; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·150·(-1)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*150}=\frac{0-10\sqrt{6}}{300}
=-\frac{10\sqrt{6}}{300}
=-\frac{\sqrt{6}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*150}=\frac{0+10\sqrt{6}}{300}
=\frac{10\sqrt{6}}{300}
=\frac{\sqrt{6}}{30}
$