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x(2x-7)=6
We move all terms to the left:
x(2x-7)-(6)=0
We multiply parentheses
2x^2-7x-6=0
a = 2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·2·(-6)
Δ = 97
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{97}}{2*2}=\frac{7-\sqrt{97}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*2}=\frac{7+\sqrt{97}}{4} $
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