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6x^2-5x=7
We move all terms to the left:
6x^2-5x-(7)=0
a = 6; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·6·(-7)
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{-(-5)-\sqrt{193}}{2*6}=\frac{5-\sqrt{193}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*6}=\frac{5+\sqrt{193}}{12} $
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