7/9x^2-4=4

Solution for 7/9x^2-4=4 equation:

7/9x^2-4=4

We move all terms to the left:

7/9x^2-4-(4)=0


Domain of the equation: 9x^2!=0

x^2!=0/9

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

7/9x^2-8=0

We multiply all the terms by the denominator


-8*9x^2+7=0

Wy multiply elements

-72x^2+7=0

a = -72; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-72)·7
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*-72}=\frac{0-12\sqrt{14}}{-144}
=-\frac{12\sqrt{14}}{-144}
=-\frac{\sqrt{14}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*-72}=\frac{0+12\sqrt{14}}{-144}
=\frac{12\sqrt{14}}{-144}
=\frac{\sqrt{14}}{-12}
$