3/4x+2x-5/4x=-6

Solution for 3/4x+2x-5/4x=-6 equation:

3/4x+2x-5/4x=-6

We move all terms to the left:

3/4x+2x-5/4x-(-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/4x-5/4x+6=0

We multiply all the terms by the denominator


2x*4x+6*4x+3-5=0

We add all the numbers together, and all the variables

2x*4x+6*4x-2=0

Wy multiply elements

8x^2+24x-2=0

a = 8; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·8·(-2)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{10}}{2*8}=\frac{-24-8\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{10}}{2*8}=\frac{-24+8\sqrt{10}}{16}
$