1/10x+8.7=16-x

Solution for 1/10x+8.7=16-x equation:

1/10x+8.7=16-x

We move all terms to the left:

1/10x+8.7-(16-x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

1/10x-(-1x+16)+8.7=0

We get rid of parentheses

1/10x+1x-16+8.7=0

We multiply all the terms by the denominator


1x*10x-16*10x+(8.7)*10x+1=0

We multiply parentheses

1x*10x-16*10x+87x+1=0

Wy multiply elements

10x^2-160x+87x+1=0

We add all the numbers together, and all the variables

10x^2-73x+1=0

a = 10; b = -73; c = +1;
Δ = b2-4ac
Δ = -732-4·10·1
Δ = 5289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-\sqrt{5289}}{2*10}=\frac{73-\sqrt{5289}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{5289}}{2*10}=\frac{73+\sqrt{5289}}{20}
$