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6x^2+24x+24x-96=138
We move all terms to the left:
6x^2+24x+24x-96-(138)=0
We add all the numbers together, and all the variables
6x^2+48x-234=0
a = 6; b = 48; c = -234;
Δ = b2-4ac
Δ = 482-4·6·(-234)
Δ = 7920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{55}}{2*6}=\frac{-48-12\sqrt{55}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{55}}{2*6}=\frac{-48+12\sqrt{55}}{12} $
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