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6x^2-9x=135
We move all terms to the left:
6x^2-9x-(135)=0
a = 6; b = -9; c = -135;
Δ = b2-4ac
Δ = -92-4·6·(-135)
Δ = 3321
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{41}}{2*6}=\frac{9-9\sqrt{41}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{41}}{2*6}=\frac{9+9\sqrt{41}}{12} $
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