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x(7x-11)=6
We move all terms to the left:
x(7x-11)-(6)=0
We multiply parentheses
7x^2-11x-6=0
a = 7; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·7·(-6)
Δ = 289
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*7}=\frac{-6}{14} =-3/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*7}=\frac{28}{14} =2 $
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