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5x^2-90x-12x-186=0
We add all the numbers together, and all the variables
5x^2-102x-186=0
a = 5; b = -102; c = -186;
Δ = b2-4ac
Δ = -1022-4·5·(-186)
Δ = 14124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14124}=\sqrt{4*3531}=\sqrt{4}*\sqrt{3531}=2\sqrt{3531}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{3531}}{2*5}=\frac{102-2\sqrt{3531}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{3531}}{2*5}=\frac{102+2\sqrt{3531}}{10} $
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