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8.6x(4.4x-11)=54
We move all terms to the left:
8.6x(4.4x-11)-(54)=0
We multiply parentheses
32x^2-88x-54=0
a = 32; b = -88; c = -54;
Δ = b2-4ac
Δ = -882-4·32·(-54)
Δ = 14656
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14656}=\sqrt{64*229}=\sqrt{64}*\sqrt{229}=8\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{229}}{2*32}=\frac{88-8\sqrt{229}}{64} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{229}}{2*32}=\frac{88+8\sqrt{229}}{64} $
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