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05x-3=3/4x+4
We move all terms to the left:
05x-3-(3/4x+4)=0
Domain of the equation: 4x+4)!=0We get rid of parentheses
x∈R
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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