-1/2x+1-7/4x=-5/4

Solution for -1/2x+1-7/4x=-5/4 equation:

-1/2x+1-7/4x=-5/4

We move all terms to the left:

-1/2x+1-7/4x-(-5/4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-1/2x-7/4x+1+5/4=0

We calculate fractions


(-64x)/128x^2+(-14x)/128x^2+10x/128x^2+1=0

We multiply all the terms by the denominator


(-64x)+(-14x)+10x+1*128x^2=0

We add all the numbers together, and all the variables

10x+(-64x)+(-14x)+1*128x^2=0

Wy multiply elements

128x^2+10x+(-64x)+(-14x)=0

We get rid of parentheses

128x^2+10x-64x-14x=0

We add all the numbers together, and all the variables

128x^2-68x=0

a = 128; b = -68; c = 0;
Δ = b2-4ac
Δ = -682-4·128·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-68}{2*128}=\frac{0}{256}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+68}{2*128}=\frac{136}{256}
=17/32
$