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6x^2-15x=27
We move all terms to the left:
6x^2-15x-(27)=0
a = 6; b = -15; c = -27;
Δ = b2-4ac
Δ = -152-4·6·(-27)
Δ = 873
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{97}}{2*6}=\frac{15-3\sqrt{97}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{97}}{2*6}=\frac{15+3\sqrt{97}}{12} $
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