5/4x+2/8x=45/12

Solution for 5/4x+2/8x=45/12 equation:

5/4x+2/8x=45/12

We move all terms to the left:

5/4x+2/8x-(45/12)=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

5/4x+2/8x-(+45/12)=0

We get rid of parentheses

5/4x+2/8x-45/12=0

We calculate fractions


(-11520x^2)/384x^2+480x/384x^2+96x/384x^2=0

We multiply all the terms by the denominator


(-11520x^2)+480x+96x=0

We add all the numbers together, and all the variables

(-11520x^2)+576x=0

We get rid of parentheses

-11520x^2+576x=0

a = -11520; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·(-11520)·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*-11520}=\frac{-1152}{-23040}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*-11520}=\frac{0}{-23040}
=0
$