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5x+19=4/3x+24
We move all terms to the left:
5x+19-(4/3x+24)=0
Domain of the equation: 3x+24)!=0We get rid of parentheses
x∈R
5x-4/3x-24+19=0
We multiply all the terms by the denominator
5x*3x-24*3x+19*3x-4=0
Wy multiply elements
15x^2-72x+57x-4=0
We add all the numbers together, and all the variables
15x^2-15x-4=0
a = 15; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·15·(-4)
Δ = 465
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{465}}{2*15}=\frac{15-\sqrt{465}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{465}}{2*15}=\frac{15+\sqrt{465}}{30} $
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