1/4x-7/8x=20-65

Solution for 1/4x-7/8x=20-65 equation:

1/4x-7/8x=20-65

We move all terms to the left:

1/4x-7/8x-(20-65)=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

1/4x-7/8x-(-45)=0

We add all the numbers together, and all the variables

1/4x-7/8x+45=0

We calculate fractions


8x/32x^2+(-28x)/32x^2+45=0

We multiply all the terms by the denominator


8x+(-28x)+45*32x^2=0

Wy multiply elements

1440x^2+8x+(-28x)=0

We get rid of parentheses

1440x^2+8x-28x=0

We add all the numbers together, and all the variables

1440x^2-20x=0

a = 1440; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·1440·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*1440}=\frac{0}{2880}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*1440}=\frac{40}{2880}
=1/72
$