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4+6x(4x-6)=92
We move all terms to the left:
4+6x(4x-6)-(92)=0
We add all the numbers together, and all the variables
6x(4x-6)-88=0
We multiply parentheses
24x^2-36x-88=0
a = 24; b = -36; c = -88;
Δ = b2-4ac
Δ = -362-4·24·(-88)
Δ = 9744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9744}=\sqrt{16*609}=\sqrt{16}*\sqrt{609}=4\sqrt{609}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{609}}{2*24}=\frac{36-4\sqrt{609}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{609}}{2*24}=\frac{36+4\sqrt{609}}{48} $
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