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(3x-2)2x+7=101
We move all terms to the left:
(3x-2)2x+7-(101)=0
We add all the numbers together, and all the variables
(3x-2)2x-94=0
We multiply parentheses
6x^2-4x-94=0
a = 6; b = -4; c = -94;
Δ = b2-4ac
Δ = -42-4·6·(-94)
Δ = 2272
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{142}}{2*6}=\frac{4-4\sqrt{142}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{142}}{2*6}=\frac{4+4\sqrt{142}}{12} $
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