3/4x+5x=-9

Solution for 3/4x+5x=-9 equation:

3/4x+5x=-9

We move all terms to the left:

3/4x+5x-(-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+3/4x+9=0

We multiply all the terms by the denominator


5x*4x+9*4x+3=0

Wy multiply elements

20x^2+36x+3=0

a = 20; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·20·3
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{66}}{2*20}=\frac{-36-4\sqrt{66}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{66}}{2*20}=\frac{-36+4\sqrt{66}}{40}
$