9.8x-13.8=2.7-1/5x

Solution for 9.8x-13.8=2.7-1/5x equation:

9.8x-13.8=2.7-1/5x

We move all terms to the left:

9.8x-13.8-(2.7-1/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9.8x-(-1/5x+2.7)-13.8=0

We get rid of parentheses

9.8x+1/5x-2.7-13.8=0

We multiply all the terms by the denominator


(9.8x)*5x-(2.7)*5x-(13.8)*5x+1=0

We add all the numbers together, and all the variables

(+9.8x)*5x-(2.7)*5x-(13.8)*5x+1=0

We multiply parentheses

45x^2-13.5x-69x+1=0

We add all the numbers together, and all the variables

45x^2-82.5x+1=0

a = 45; b = -82.5; c = +1;
Δ = b2-4ac
Δ = -82.52-4·45·1
Δ = 6626.25
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{-(-82.5)-\sqrt{6626.25}}{2*45}=\frac{82.5-\sqrt{6626.25}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82.5)+\sqrt{6626.25}}{2*45}=\frac{82.5+\sqrt{6626.25}}{90}
$