6/5x+2/10x=15/8

Solution for 6/5x+2/10x=15/8 equation:

6/5x+2/10x=15/8

We move all terms to the left:

6/5x+2/10x-(15/8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

6/5x+2/10x-(+15/8)=0

We get rid of parentheses

6/5x+2/10x-15/8=0

We calculate fractions


(-750x^2)/3200x^2+3840x/3200x^2+640x/3200x^2=0

We multiply all the terms by the denominator


(-750x^2)+3840x+640x=0

We add all the numbers together, and all the variables

(-750x^2)+4480x=0

We get rid of parentheses

-750x^2+4480x=0

a = -750; b = 4480; c = 0;
Δ = b2-4ac
Δ = 44802-4·(-750)·0
Δ = 20070400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20070400}=4480$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4480)-4480}{2*-750}=\frac{-8960}{-1500}
=5+73/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4480)+4480}{2*-750}=\frac{0}{-1500}
=0
$