2/5x-17.7=-2.5x+20

Solution for 2/5x-17.7=-2.5x+20 equation:

2/5x-17.7=-2.5x+20

We move all terms to the left:

2/5x-17.7-(-2.5x+20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x+2.5x-20-17.7=0

We multiply all the terms by the denominator


(2.5x)*5x-20*5x-(17.7)*5x+2=0

We add all the numbers together, and all the variables

(+2.5x)*5x-20*5x-(17.7)*5x+2=0

We multiply parentheses

10x^2-20*5x-88.5x+2=0

Wy multiply elements

10x^2-100x-88.5x+2=0

We add all the numbers together, and all the variables

10x^2-188.5x+2=0

a = 10; b = -188.5; c = +2;
Δ = b2-4ac
Δ = -188.52-4·10·2
Δ = 35452.25
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{-(-188.5)-\sqrt{35452.25}}{2*10}=\frac{188.5-\sqrt{35452.25}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-188.5)+\sqrt{35452.25}}{2*10}=\frac{188.5+\sqrt{35452.25}}{20}
$