1/5x-5=10-3/4x

Solution for 1/5x-5=10-3/4x equation:

1/5x-5=10-3/4x

We move all terms to the left:

1/5x-5-(10-3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(-3/4x+10)-5=0

We get rid of parentheses

1/5x+3/4x-10-5=0

We calculate fractions


4x/20x^2+15x/20x^2-10-5=0

We add all the numbers together, and all the variables

4x/20x^2+15x/20x^2-15=0

We multiply all the terms by the denominator


4x+15x-15*20x^2=0

We add all the numbers together, and all the variables

19x-15*20x^2=0

Wy multiply elements

-300x^2+19x=0

a = -300; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-300)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-300}=\frac{-38}{-600}
=19/300
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-300}=\frac{0}{-600}
=0
$