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5x^2-36x-55=0
a = 5; b = -36; c = -55;
Δ = b2-4ac
Δ = -362-4·5·(-55)
Δ = 2396
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2396}=\sqrt{4*599}=\sqrt{4}*\sqrt{599}=2\sqrt{599}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{599}}{2*5}=\frac{36-2\sqrt{599}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{599}}{2*5}=\frac{36+2\sqrt{599}}{10} $
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