-2/5x+10=3/4x

Solution for -2/5x+10=3/4x equation:

-2/5x+10=3/4x

We move all terms to the left:

-2/5x+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

-2/5x-(+3/4x)+10=0

We get rid of parentheses

-2/5x-3/4x+10=0

We calculate fractions


(-8x)/20x^2+(-15x)/20x^2+10=0

We multiply all the terms by the denominator


(-8x)+(-15x)+10*20x^2=0

Wy multiply elements

200x^2+(-8x)+(-15x)=0

We get rid of parentheses

200x^2-8x-15x=0

We add all the numbers together, and all the variables

200x^2-23x=0

a = 200; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·200·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*200}=\frac{0}{400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*200}=\frac{46}{400}
=23/200
$