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144x^2-2940x+5184=0
a = 144; b = -2940; c = +5184;
Δ = b2-4ac
Δ = -29402-4·144·5184
Δ = 5657616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5657616}=\sqrt{144*39289}=\sqrt{144}*\sqrt{39289}=12\sqrt{39289}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2940)-12\sqrt{39289}}{2*144}=\frac{2940-12\sqrt{39289}}{288} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2940)+12\sqrt{39289}}{2*144}=\frac{2940+12\sqrt{39289}}{288} $
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