(7/9)x=5/9

Solution for (7/9)x=5/9 equation:

(7/9)x=5/9

We move all terms to the left:

(7/9)x-(5/9)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+7/9)x-(+5/9)=0

We multiply parentheses

7x^2-(+5/9)=0

We get rid of parentheses

7x^2-5/9=0

We multiply all the terms by the denominator


7x^2*9-5=0

Wy multiply elements

63x^2-5=0

a = 63; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·63·(-5)
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*63}=\frac{0-6\sqrt{35}}{126}
=-\frac{6\sqrt{35}}{126}
=-\frac{\sqrt{35}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*63}=\frac{0+6\sqrt{35}}{126}
=\frac{6\sqrt{35}}{126}
=\frac{\sqrt{35}}{21}
$