2/5x-177/10=-5/2x+20

Solution for 2/5x-177/10=-5/2x+20 equation:

2/5x-177/10=-5/2x+20

We move all terms to the left:

2/5x-177/10-(-5/2x+20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+20)!=0

x∈R


We get rid of parentheses

2/5x+5/2x-20-177/10=0

We calculate fractions


(-3540x^2)/100x^2+40x/100x^2+250x/100x^2-20=0

We multiply all the terms by the denominator


(-3540x^2)+40x+250x-20*100x^2=0

We add all the numbers together, and all the variables

(-3540x^2)+290x-20*100x^2=0

Wy multiply elements

(-3540x^2)-2000x^2+290x=0

We get rid of parentheses

-3540x^2-2000x^2+290x=0

We add all the numbers together, and all the variables

-5540x^2+290x=0

a = -5540; b = 290; c = 0;
Δ = b2-4ac
Δ = 2902-4·(-5540)·0
Δ = 84100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{84100}=290$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(290)-290}{2*-5540}=\frac{-580}{-11080}
=29/554
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(290)+290}{2*-5540}=\frac{0}{-11080}
=0
$