3/5x+7/4=3/10x+7

Solution for 3/5x+7/4=3/10x+7 equation:

3/5x+7/4=3/10x+7

We move all terms to the left:

3/5x+7/4-(3/10x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+7)!=0

x∈R


We get rid of parentheses

3/5x-3/10x-7+7/4=0

We calculate fractions


350x^2/800x^2+480x/800x^2+(-240x)/800x^2-7=0

We multiply all the terms by the denominator


350x^2+480x+(-240x)-7*800x^2=0

Wy multiply elements

350x^2-5600x^2+480x+(-240x)=0

We get rid of parentheses

350x^2-5600x^2+480x-240x=0

We add all the numbers together, and all the variables

-5250x^2+240x=0

a = -5250; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-5250)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-5250}=\frac{-480}{-10500}
=8/175
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-5250}=\frac{0}{-10500}
=0
$