05x-3=3/4x+4

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Solution for 05x-3=3/4x+4 equation:



05x-3=3/4x+4
We move all terms to the left:
05x-3-(3/4x+4)=0
Domain of the equation: 4x+4)!=0
x∈R
We get rid of parentheses
05x-3/4x-4-3=0
We multiply all the terms by the denominator
05x*4x-4*4x-3*4x-3=0
Wy multiply elements
20x^2-16x-12x-3=0
We add all the numbers together, and all the variables
20x^2-28x-3=0
a = 20; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·20·(-3)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-32}{2*20}=\frac{-4}{40} =-1/10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+32}{2*20}=\frac{60}{40} =1+1/2 $

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