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6x^2+9x-150=0
a = 6; b = 9; c = -150;
Δ = b2-4ac
Δ = 92-4·6·(-150)
Δ = 3681
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3681}=\sqrt{9*409}=\sqrt{9}*\sqrt{409}=3\sqrt{409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{409}}{2*6}=\frac{-9-3\sqrt{409}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{409}}{2*6}=\frac{-9+3\sqrt{409}}{12} $
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