-4/5x+5/4=-1/4x+4

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Solution for -4/5x+5/4=-1/4x+4 equation:



-4/5x+5/4=-1/4x+4
We move all terms to the left:
-4/5x+5/4-(-1/4x+4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x+4)!=0
x∈R
We get rid of parentheses
-4/5x+1/4x-4+5/4=0
We calculate fractions
(-256x)/320x^2+5x/320x^2+25x/320x^2-4=0
We multiply all the terms by the denominator
(-256x)+5x+25x-4*320x^2=0
We add all the numbers together, and all the variables
30x+(-256x)-4*320x^2=0
Wy multiply elements
-1280x^2+30x+(-256x)=0
We get rid of parentheses
-1280x^2+30x-256x=0
We add all the numbers together, and all the variables
-1280x^2-226x=0
a = -1280; b = -226; c = 0;
Δ = b2-4ac
Δ = -2262-4·(-1280)·0
Δ = 51076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51076}=226$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-226)-226}{2*-1280}=\frac{0}{-2560} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-226)+226}{2*-1280}=\frac{452}{-2560} =-113/640 $

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