3/4x=x-9

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

3/4x=x-9

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-x+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}
$