-7/4x-1/4-3/2x=-43/16

Solution for -7/4x-1/4-3/2x=-43/16 equation:

-7/4x-1/4-3/2x=-43/16

We move all terms to the left:

-7/4x-1/4-3/2x-(-43/16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-7/4x-3/2x-1/4+43/16=0

We calculate fractions


(-256x^2)/2048x^2+2752x^2/2048x^2+(-3584x)/2048x^2+(-3072x)/2048x^2=0

We multiply all the terms by the denominator


(-256x^2)+2752x^2+(-3584x)+(-3072x)=0

We add all the numbers together, and all the variables

2752x^2+(-256x^2)+(-3584x)+(-3072x)=0

We get rid of parentheses

2752x^2-256x^2-3584x-3072x=0

We add all the numbers together, and all the variables

2496x^2-6656x=0

a = 2496; b = -6656; c = 0;
Δ = b2-4ac
Δ = -66562-4·2496·0
Δ = 44302336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44302336}=6656$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6656)-6656}{2*2496}=\frac{0}{4992}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6656)+6656}{2*2496}=\frac{13312}{4992}
=2+2/3
$