7/4x=2/10x+6

Solution for 7/4x=2/10x+6 equation:

7/4x=2/10x+6

We move all terms to the left:

7/4x-(2/10x+6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x+6)!=0

x∈R


We get rid of parentheses

7/4x-2/10x-6=0

We calculate fractions


70x/40x^2+(-8x)/40x^2-6=0

We multiply all the terms by the denominator


70x+(-8x)-6*40x^2=0

Wy multiply elements

-240x^2+70x+(-8x)=0

We get rid of parentheses

-240x^2+70x-8x=0

We add all the numbers together, and all the variables

-240x^2+62x=0

a = -240; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-240)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-240}=\frac{-124}{-480}
=31/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-240}=\frac{0}{-480}
=0
$