X=7/9x+4

Solution for X=7/9x+4 equation:

X=7/9X+4

We move all terms to the left:

X-(7/9X+4)=0


Domain of the equation: 9X+4)!=0

X∈R


We get rid of parentheses

X-7/9X-4=0

We multiply all the terms by the denominator


X*9X-4*9X-7=0

Wy multiply elements

9X^2-36X-7=0

a = 9; b = -36; c = -7;
Δ = b2-4ac
Δ = -362-4·9·(-7)
Δ = 1548
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:

$\sqrt{\Delta}=\sqrt{1548}=\sqrt{36*43}=\sqrt{36}*\sqrt{43}=6\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{43}}{2*9}=\frac{36-6\sqrt{43}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{43}}{2*9}=\frac{36+6\sqrt{43}}{18}
$