X=1/10y+2=-16

Solution for X=1/10y+2=-16 equation:

X=1/10X+2=-16

We move all terms to the left:

X-(1/10X+2)=0


Domain of the equation: 10X+2)!=0

X∈R


We get rid of parentheses

X-1/10X-2=0

We multiply all the terms by the denominator


X*10X-2*10X-1=0

Wy multiply elements

10X^2-20X-1=0

a = 10; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·10·(-1)
Δ = 440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*10}=\frac{20-2\sqrt{110}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*10}=\frac{20+2\sqrt{110}}{20}
$