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1.5x+4=1/5x+9
We move all terms to the left:
1.5x+4-(1/5x+9)=0
Domain of the equation: 5x+9)!=0We get rid of parentheses
x∈R
1.5x-1/5x-9+4=0
We multiply all the terms by the denominator
(1.5x)*5x-9*5x+4*5x-1=0
We add all the numbers together, and all the variables
(+1.5x)*5x-9*5x+4*5x-1=0
We multiply parentheses
5x^2-9*5x+4*5x-1=0
Wy multiply elements
5x^2-45x+20x-1=0
We add all the numbers together, and all the variables
5x^2-25x-1=0
a = 5; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·5·(-1)
Δ = 645
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{-(-25)-\sqrt{645}}{2*5}=\frac{25-\sqrt{645}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{645}}{2*5}=\frac{25+\sqrt{645}}{10} $
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