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0=6x^2-72x+140
We move all terms to the left:
0-(6x^2-72x+140)=0
We add all the numbers together, and all the variables
-(6x^2-72x+140)=0
We get rid of parentheses
-6x^2+72x-140=0
a = -6; b = 72; c = -140;
Δ = b2-4ac
Δ = 722-4·(-6)·(-140)
Δ = 1824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{114}}{2*-6}=\frac{-72-4\sqrt{114}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{114}}{2*-6}=\frac{-72+4\sqrt{114}}{-12} $
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