19/45x^2-38=0

Solution for 19/45x^2-38=0 equation:

19/45x^2-38=0


Domain of the equation: 45x^2!=0

x^2!=0/45

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-38*45x^2+19=0

Wy multiply elements

-1710x^2+19=0

a = -1710; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-1710)·19
Δ = 129960
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:

$\sqrt{\Delta}=\sqrt{129960}=\sqrt{12996*10}=\sqrt{12996}*\sqrt{10}=114\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-114\sqrt{10}}{2*-1710}=\frac{0-114\sqrt{10}}{-3420}
=-\frac{114\sqrt{10}}{-3420}
=-\frac{\sqrt{10}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+114\sqrt{10}}{2*-1710}=\frac{0+114\sqrt{10}}{-3420}
=\frac{114\sqrt{10}}{-3420}
=\frac{\sqrt{10}}{-30}
$