2-3/4x-1/8x=9

Solution for 2-3/4x-1/8x=9 equation:

2-3/4x-1/8x=9

We move all terms to the left:

2-3/4x-1/8x-(9)=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-7=0

We calculate fractions


(-24x)/32x^2+(-4x)/32x^2-7=0

We multiply all the terms by the denominator


(-24x)+(-4x)-7*32x^2=0

Wy multiply elements

-224x^2+(-24x)+(-4x)=0

We get rid of parentheses

-224x^2-24x-4x=0

We add all the numbers together, and all the variables

-224x^2-28x=0

a = -224; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-224)·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*-224}=\frac{0}{-448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-224}=\frac{56}{-448}
=-1/8
$