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12x^2-12x=25
We move all terms to the left:
12x^2-12x-(25)=0
a = 12; b = -12; c = -25;
Δ = b2-4ac
Δ = -122-4·12·(-25)
Δ = 1344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{21}}{2*12}=\frac{12-8\sqrt{21}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{21}}{2*12}=\frac{12+8\sqrt{21}}{24} $
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