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2x^2+33x-63=0
a = 2; b = 33; c = -63;
Δ = b2-4ac
Δ = 332-4·2·(-63)
Δ = 1593
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{177}}{2*2}=\frac{-33-3\sqrt{177}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{177}}{2*2}=\frac{-33+3\sqrt{177}}{4} $
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