x=3/4x+9

Solution for x=3/4x+9 equation:

x=3/4x+9

We move all terms to the left:

x-(3/4x+9)=0


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

x∈R


We get rid of parentheses

x-3/4x-9=0

We multiply all the terms by the denominator


x*4x-9*4x-3=0

Wy multiply elements

4x^2-36x-3=0

a = 4; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·4·(-3)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*4}=\frac{36-8\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*4}=\frac{36+8\sqrt{21}}{8}
$