6/5*x+2/3*x=28

Solution for 6/5*x+2/3*x=28 equation:

6/5x+2/3x=28

We move all terms to the left:

6/5x+2/3x-(28)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


18x/15x^2+10x/15x^2-28=0

We multiply all the terms by the denominator


18x+10x-28*15x^2=0

We add all the numbers together, and all the variables

28x-28*15x^2=0

Wy multiply elements

-420x^2+28x=0

a = -420; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-420)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-420}=\frac{-56}{-840}
=1/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-420}=\frac{0}{-840}
=0
$