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11x^2-30x+3=0
a = 11; b = -30; c = +3;
Δ = b2-4ac
Δ = -302-4·11·3
Δ = 768
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-16\sqrt{3}}{2*11}=\frac{30-16\sqrt{3}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+16\sqrt{3}}{2*11}=\frac{30+16\sqrt{3}}{22} $
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