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4x+14=2/3x+19
We move all terms to the left:
4x+14-(2/3x+19)=0
Domain of the equation: 3x+19)!=0We get rid of parentheses
x∈R
4x-2/3x-19+14=0
We multiply all the terms by the denominator
4x*3x-19*3x+14*3x-2=0
Wy multiply elements
12x^2-57x+42x-2=0
We add all the numbers together, and all the variables
12x^2-15x-2=0
a = 12; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·12·(-2)
Δ = 321
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{321}}{2*12}=\frac{15-\sqrt{321}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{321}}{2*12}=\frac{15+\sqrt{321}}{24} $
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