0.4x+101=3/5x+12

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Solution for 0.4x+101=3/5x+12 equation:



0.4x+101=3/5x+12
We move all terms to the left:
0.4x+101-(3/5x+12)=0
Domain of the equation: 5x+12)!=0
x∈R
We get rid of parentheses
0.4x-3/5x-12+101=0
We multiply all the terms by the denominator
(0.4x)*5x-12*5x+101*5x-3=0
We add all the numbers together, and all the variables
(+0.4x)*5x-12*5x+101*5x-3=0
We multiply parentheses
0x^2-12*5x+101*5x-3=0
Wy multiply elements
0x^2-60x+505x-3=0
We add all the numbers together, and all the variables
x^2+445x-3=0
a = 1; b = 445; c = -3;
Δ = b2-4ac
Δ = 4452-4·1·(-3)
Δ = 198037
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{-(445)-\sqrt{198037}}{2*1}=\frac{-445-\sqrt{198037}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(445)+\sqrt{198037}}{2*1}=\frac{-445+\sqrt{198037}}{2} $

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