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3x^2-7x/2=3
We move all terms to the left:
3x^2-7x/2-(3)=0
We multiply all the terms by the denominator
3x^2*2-7x-3*2=0
We add all the numbers together, and all the variables
3x^2*2-7x-6=0
Wy multiply elements
6x^2-7x-6=0
a = 6; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·6·(-6)
Δ = 193
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{-(-7)-\sqrt{193}}{2*6}=\frac{7-\sqrt{193}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{193}}{2*6}=\frac{7+\sqrt{193}}{12} $
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