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4/3x-5=-2x-36
We move all terms to the left:
4/3x-5-(-2x-36)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
4/3x+2x+36-5=0
We multiply all the terms by the denominator
2x*3x+36*3x-5*3x+4=0
Wy multiply elements
6x^2+108x-15x+4=0
We add all the numbers together, and all the variables
6x^2+93x+4=0
a = 6; b = 93; c = +4;
Δ = b2-4ac
Δ = 932-4·6·4
Δ = 8553
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{-(93)-\sqrt{8553}}{2*6}=\frac{-93-\sqrt{8553}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+\sqrt{8553}}{2*6}=\frac{-93+\sqrt{8553}}{12} $
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