2/9x=x+7

Solution for 2/9x=x+7 equation:

2/9x=x+7

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

2/9x-x-7=0

We multiply all the terms by the denominator


-x*9x-7*9x+2=0

Wy multiply elements

-9x^2-63x+2=0

a = -9; b = -63; c = +2;
Δ = b2-4ac
Δ = -632-4·(-9)·2
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{449}}{2*-9}=\frac{63-3\sqrt{449}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{449}}{2*-9}=\frac{63+3\sqrt{449}}{-18}
$