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/6x+5=4x+17
We move all terms to the left:
/6x+5-(4x+17)=0
Domain of the equation: 6x!=0We get rid of parentheses
x!=0/6
x!=0
x∈R
/6x-4x-17+5=0
We multiply all the terms by the denominator
-4x*6x-17*6x+5*6x+=0
We add all the numbers together, and all the variables
-4x*6x-17*6x+5*6x=0
Wy multiply elements
-24x^2-102x+30x=0
We add all the numbers together, and all the variables
-24x^2-72x=0
a = -24; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-24)·0
Δ = 5184
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{5184}=72$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-24}=\frac{0}{-48} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-24}=\frac{144}{-48} =-3 $
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