2/5x-2+4x=-3/5x-12

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Solution for 2/5x-2+4x=-3/5x-12 equation:



2/5x-2+4x=-3/5x-12
We move all terms to the left:
2/5x-2+4x-(-3/5x-12)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 5x-12)!=0
x∈R
We add all the numbers together, and all the variables
4x+2/5x-(-3/5x-12)-2=0
We get rid of parentheses
4x+2/5x+3/5x+12-2=0
We multiply all the terms by the denominator
4x*5x+12*5x-2*5x+2+3=0
We add all the numbers together, and all the variables
4x*5x+12*5x-2*5x+5=0
Wy multiply elements
20x^2+60x-10x+5=0
We add all the numbers together, and all the variables
20x^2+50x+5=0
a = 20; b = 50; c = +5;
Δ = b2-4ac
Δ = 502-4·20·5
Δ = 2100
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:
$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{21}}{2*20}=\frac{-50-10\sqrt{21}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{21}}{2*20}=\frac{-50+10\sqrt{21}}{40} $

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