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5x^2-162x+210=0
a = 5; b = -162; c = +210;
Δ = b2-4ac
Δ = -1622-4·5·210
Δ = 22044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{22044}=\sqrt{4*5511}=\sqrt{4}*\sqrt{5511}=2\sqrt{5511}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-2\sqrt{5511}}{2*5}=\frac{162-2\sqrt{5511}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+2\sqrt{5511}}{2*5}=\frac{162+2\sqrt{5511}}{10} $
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