5/9=4x2

Solution for 5/9=4x2 equation:

5/9=4x^2

We move all terms to the left:

5/9-(4x^2)=0

We multiply all the terms by the denominator


-4x^2*9+5=0

Wy multiply elements

-36x^2+5=0

a = -36; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-36)·5
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-36}=\frac{0-12\sqrt{5}}{-72}
=-\frac{12\sqrt{5}}{-72}
=-\frac{\sqrt{5}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-36}=\frac{0+12\sqrt{5}}{-72}
=\frac{12\sqrt{5}}{-72}
=\frac{\sqrt{5}}{-6}
$