1-7/2x^2+36=0

Solution for 1-7/2x^2+36=0 equation:

1-7/2x^2+36=0


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

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

-7/2x^2+37=0

We multiply all the terms by the denominator


37*2x^2-7=0

Wy multiply elements

74x^2-7=0

a = 74; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·74·(-7)
Δ = 2072
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:

$\sqrt{\Delta}=\sqrt{2072}=\sqrt{4*518}=\sqrt{4}*\sqrt{518}=2\sqrt{518}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{518}}{2*74}=\frac{0-2\sqrt{518}}{148}
=-\frac{2\sqrt{518}}{148}
=-\frac{\sqrt{518}}{74}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{518}}{2*74}=\frac{0+2\sqrt{518}}{148}
=\frac{2\sqrt{518}}{148}
=\frac{\sqrt{518}}{74}
$