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4x(x-6)=-24
We move all terms to the left:
4x(x-6)-(-24)=0
We add all the numbers together, and all the variables
4x(x-6)+24=0
We multiply parentheses
4x^2-24x+24=0
a = 4; b = -24; c = +24;
Δ = b2-4ac
Δ = -242-4·4·24
Δ = 192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{3}}{2*4}=\frac{24-8\sqrt{3}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{3}}{2*4}=\frac{24+8\sqrt{3}}{8} $
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