3/4x-4+8x=-22

Solution for 3/4x-4+8x=-22 equation:

3/4x-4+8x=-22

We move all terms to the left:

3/4x-4+8x-(-22)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

8x+3/4x+18=0

We multiply all the terms by the denominator


8x*4x+18*4x+3=0

Wy multiply elements

32x^2+72x+3=0

a = 32; b = 72; c = +3;
Δ = b2-4ac
Δ = 722-4·32·3
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-40\sqrt{3}}{2*32}=\frac{-72-40\sqrt{3}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+40\sqrt{3}}{2*32}=\frac{-72+40\sqrt{3}}{64}
$