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7x^2-144x+63=0
a = 7; b = -144; c = +63;
Δ = b2-4ac
Δ = -1442-4·7·63
Δ = 18972
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18972}=\sqrt{36*527}=\sqrt{36}*\sqrt{527}=6\sqrt{527}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-6\sqrt{527}}{2*7}=\frac{144-6\sqrt{527}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+6\sqrt{527}}{2*7}=\frac{144+6\sqrt{527}}{14} $
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