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3x^2+5x/3=4
We move all terms to the left:
3x^2+5x/3-(4)=0
We multiply all the terms by the denominator
3x^2*3+5x-4*3=0
We add all the numbers together, and all the variables
3x^2*3+5x-12=0
Wy multiply elements
9x^2+5x-12=0
a = 9; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·9·(-12)
Δ = 457
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{-(5)-\sqrt{457}}{2*9}=\frac{-5-\sqrt{457}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{457}}{2*9}=\frac{-5+\sqrt{457}}{18} $
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