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2x^2-72x-972=0
a = 2; b = -72; c = -972;
Δ = b2-4ac
Δ = -722-4·2·(-972)
Δ = 12960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12960}=\sqrt{1296*10}=\sqrt{1296}*\sqrt{10}=36\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-36\sqrt{10}}{2*2}=\frac{72-36\sqrt{10}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+36\sqrt{10}}{2*2}=\frac{72+36\sqrt{10}}{4} $
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