4/5x+1/2x+2=10

Solution for 4/5x+1/2x+2=10 equation:

4/5x+1/2x+2=10

We move all terms to the left:

4/5x+1/2x+2-(10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x+1/2x-8=0

We calculate fractions


8x/10x^2+5x/10x^2-8=0

We multiply all the terms by the denominator


8x+5x-8*10x^2=0

We add all the numbers together, and all the variables

13x-8*10x^2=0

Wy multiply elements

-80x^2+13x=0

a = -80; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-80)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-80}=\frac{-26}{-160}
=13/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-80}=\frac{0}{-160}
=0
$