6.25x-1/4x+7.3x=-2.25

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Solution for 6.25x-1/4x+7.3x=-2.25 equation:



6.25x-1/4x+7.3x=-2.25
We move all terms to the left:
6.25x-1/4x+7.3x-(-2.25)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
13.55x-1/4x+2.25=0
We multiply all the terms by the denominator
(13.55x)*4x+(2.25)*4x-1=0
We add all the numbers together, and all the variables
(+13.55x)*4x+(2.25)*4x-1=0
We multiply parentheses
52x^2+9x-1=0
a = 52; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·52·(-1)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*52}=\frac{-26}{104} =-1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*52}=\frac{8}{104} =1/13 $

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