3/5x+8/10x=45/15

Solution for 3/5x+8/10x=45/15 equation:

3/5x+8/10x=45/15

We move all terms to the left:

3/5x+8/10x-(45/15)=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

3/5x+8/10x-3=0

We calculate fractions


30x/50x^2+40x/50x^2-3=0

We multiply all the terms by the denominator


30x+40x-3*50x^2=0

We add all the numbers together, and all the variables

70x-3*50x^2=0

Wy multiply elements

-150x^2+70x=0

a = -150; b = 70; c = 0;
Δ = b2-4ac
Δ = 702-4·(-150)·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*-150}=\frac{-140}{-300}
=7/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70}{2*-150}=\frac{0}{-300}
=0
$