9=3/4x+x

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

9=3/4x+x

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

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 = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{78}}{2*-4}=\frac{-36-4\sqrt{78}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{78}}{2*-4}=\frac{-36+4\sqrt{78}}{-8}
$