-5/4x-3/8=1/2x+6

Solution for -5/4x-3/8=1/2x+6 equation:

-5/4x-3/8=1/2x+6

We move all terms to the left:

-5/4x-3/8-(1/2x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

-5/4x-1/2x-6-3/8=0

We calculate fractions


(-48x^2)/512x^2+(-640x)/512x^2+(-256x)/512x^2-6=0

We multiply all the terms by the denominator


(-48x^2)+(-640x)+(-256x)-6*512x^2=0

Wy multiply elements

(-48x^2)-3072x^2+(-640x)+(-256x)=0

We get rid of parentheses

-48x^2-3072x^2-640x-256x=0

We add all the numbers together, and all the variables

-3120x^2-896x=0

a = -3120; b = -896; c = 0;
Δ = b2-4ac
Δ = -8962-4·(-3120)·0
Δ = 802816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{802816}=896$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-896)-896}{2*-3120}=\frac{0}{-6240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-896)+896}{2*-3120}=\frac{1792}{-6240}
=-56/195
$