4/5x+6/10x=14

Solution for 4/5x+6/10x=14 equation:

4/5x+6/10x=14

We move all terms to the left:

4/5x+6/10x-(14)=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 calculate fractions


40x/50x^2+30x/50x^2-14=0

We multiply all the terms by the denominator


40x+30x-14*50x^2=0

We add all the numbers together, and all the variables

70x-14*50x^2=0

Wy multiply elements

-700x^2+70x=0

a = -700; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-700)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70}{2*-700}=\frac{-140}{-1400}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-700}=\frac{0}{-1400}
=0
$