3/4x+1/8x-6=-5

Solution for 3/4x+1/8x-6=-5 equation:

3/4x+1/8x-6=-5

We move all terms to the left:

3/4x+1/8x-6-(-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+1/8x-1=0

We calculate fractions


24x/32x^2+4x/32x^2-1=0

We multiply all the terms by the denominator


24x+4x-1*32x^2=0

We add all the numbers together, and all the variables

28x-1*32x^2=0

Wy multiply elements

-32x^2+28x=0

a = -32; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-32)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-32}=\frac{-56}{-64}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-32}=\frac{0}{-64}
=0
$