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7x^2-159x-252=0
a = 7; b = -159; c = -252;
Δ = b2-4ac
Δ = -1592-4·7·(-252)
Δ = 32337
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32337}=\sqrt{9*3593}=\sqrt{9}*\sqrt{3593}=3\sqrt{3593}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-3\sqrt{3593}}{2*7}=\frac{159-3\sqrt{3593}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+3\sqrt{3593}}{2*7}=\frac{159+3\sqrt{3593}}{14} $
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