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12x^2+72x-55=0
a = 12; b = 72; c = -55;
Δ = b2-4ac
Δ = 722-4·12·(-55)
Δ = 7824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7824}=\sqrt{16*489}=\sqrt{16}*\sqrt{489}=4\sqrt{489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{489}}{2*12}=\frac{-72-4\sqrt{489}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{489}}{2*12}=\frac{-72+4\sqrt{489}}{24} $
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