-41/4x-75/8x=-190

Solution for -41/4x-75/8x=-190 equation:

-41/4x-75/8x=-190

We move all terms to the left:

-41/4x-75/8x-(-190)=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

-41/4x-75/8x+190=0

We calculate fractions


(-328x)/32x^2+(-300x)/32x^2+190=0

We multiply all the terms by the denominator


(-328x)+(-300x)+190*32x^2=0

Wy multiply elements

6080x^2+(-328x)+(-300x)=0

We get rid of parentheses

6080x^2-328x-300x=0

We add all the numbers together, and all the variables

6080x^2-628x=0

a = 6080; b = -628; c = 0;
Δ = b2-4ac
Δ = -6282-4·6080·0
Δ = 394384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{394384}=628$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-628)-628}{2*6080}=\frac{0}{12160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-628)+628}{2*6080}=\frac{1256}{12160}
=157/1520
$