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12x(4x+10)=54
We move all terms to the left:
12x(4x+10)-(54)=0
We multiply parentheses
48x^2+120x-54=0
a = 48; b = 120; c = -54;
Δ = b2-4ac
Δ = 1202-4·48·(-54)
Δ = 24768
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24768}=\sqrt{576*43}=\sqrt{576}*\sqrt{43}=24\sqrt{43}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{43}}{2*48}=\frac{-120-24\sqrt{43}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{43}}{2*48}=\frac{-120+24\sqrt{43}}{96} $
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