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-3x^2+12x+11=0
a = -3; b = 12; c = +11;
Δ = b2-4ac
Δ = 122-4·(-3)·11
Δ = 276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{69}}{2*-3}=\frac{-12-2\sqrt{69}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{69}}{2*-3}=\frac{-12+2\sqrt{69}}{-6} $
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