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5x^2-172x+63=0
a = 5; b = -172; c = +63;
Δ = b2-4ac
Δ = -1722-4·5·63
Δ = 28324
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28324}=\sqrt{4*7081}=\sqrt{4}*\sqrt{7081}=2\sqrt{7081}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-2\sqrt{7081}}{2*5}=\frac{172-2\sqrt{7081}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+2\sqrt{7081}}{2*5}=\frac{172+2\sqrt{7081}}{10} $
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