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x/5x+3=4x+14*
We move all terms to the left:
x/5x+3-(4x+14*)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
x/5x-(+4x)+3=0
We get rid of parentheses
x/5x-4x+3=0
We multiply all the terms by the denominator
x-4x*5x+3*5x=0
Wy multiply elements
-20x^2+x+15x=0
We add all the numbers together, and all the variables
-20x^2+16x=0
a = -20; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-20)·0
Δ = 256
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{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-20}=\frac{-32}{-40} =4/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-20}=\frac{0}{-40} =0 $
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