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1/5x+3=4x
We move all terms to the left:
1/5x+3-(4x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
-4x+1/5x+3=0
We multiply all the terms by the denominator
-4x*5x+3*5x+1=0
Wy multiply elements
-20x^2+15x+1=0
a = -20; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-20)·1
Δ = 305
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{-(15)-\sqrt{305}}{2*-20}=\frac{-15-\sqrt{305}}{-40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{305}}{2*-20}=\frac{-15+\sqrt{305}}{-40} $
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