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(8x-4)3x+6x=102
We move all terms to the left:
(8x-4)3x+6x-(102)=0
We add all the numbers together, and all the variables
6x+(8x-4)3x-102=0
We multiply parentheses
24x^2+6x-12x-102=0
We add all the numbers together, and all the variables
24x^2-6x-102=0
a = 24; b = -6; c = -102;
Δ = b2-4ac
Δ = -62-4·24·(-102)
Δ = 9828
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9828}=\sqrt{36*273}=\sqrt{36}*\sqrt{273}=6\sqrt{273}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{273}}{2*24}=\frac{6-6\sqrt{273}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{273}}{2*24}=\frac{6+6\sqrt{273}}{48} $
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