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27x+108x^2=400
We move all terms to the left:
27x+108x^2-(400)=0
a = 108; b = 27; c = -400;
Δ = b2-4ac
Δ = 272-4·108·(-400)
Δ = 173529
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{173529}=\sqrt{9*19281}=\sqrt{9}*\sqrt{19281}=3\sqrt{19281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{19281}}{2*108}=\frac{-27-3\sqrt{19281}}{216} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{19281}}{2*108}=\frac{-27+3\sqrt{19281}}{216} $
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