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3x(x-1)=15
We move all terms to the left:
3x(x-1)-(15)=0
We multiply parentheses
3x^2-3x-15=0
a = 3; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·3·(-15)
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*3}=\frac{3-3\sqrt{21}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*3}=\frac{3+3\sqrt{21}}{6} $
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