15/8x-11=7/4x+1

Solution for 15/8x-11=7/4x+1 equation:

15/8x-11=7/4x+1

We move all terms to the left:

15/8x-11-(7/4x+1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

15/8x-7/4x-1-11=0

We calculate fractions


60x/32x^2+(-56x)/32x^2-1-11=0

We add all the numbers together, and all the variables

60x/32x^2+(-56x)/32x^2-12=0

We multiply all the terms by the denominator


60x+(-56x)-12*32x^2=0

Wy multiply elements

-384x^2+60x+(-56x)=0

We get rid of parentheses

-384x^2+60x-56x=0

We add all the numbers together, and all the variables

-384x^2+4x=0

a = -384; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-384)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-384}=\frac{-8}{-768}
=1/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-384}=\frac{0}{-768}
=0
$