x=-1/20x+13.6

Solution for x=-1/20x+13.6 equation:

x=-1/20x+13.6

We move all terms to the left:

x-(-1/20x+13.6)=0


Domain of the equation: 20x+13.6)!=0

x∈R


We get rid of parentheses

x+1/20x-13.6=0

We multiply all the terms by the denominator


x*20x-(13.6)*20x+1=0

We multiply parentheses

x*20x-272x+1=0

Wy multiply elements

20x^2-272x+1=0

a = 20; b = -272; c = +1;
Δ = b2-4ac
Δ = -2722-4·20·1
Δ = 73904
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:

$\sqrt{\Delta}=\sqrt{73904}=\sqrt{16*4619}=\sqrt{16}*\sqrt{4619}=4\sqrt{4619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-4\sqrt{4619}}{2*20}=\frac{272-4\sqrt{4619}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+4\sqrt{4619}}{2*20}=\frac{272+4\sqrt{4619}}{40}
$