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3(4x^2-33x-8)=0
We multiply parentheses
12x^2-99x-24=0
a = 12; b = -99; c = -24;
Δ = b2-4ac
Δ = -992-4·12·(-24)
Δ = 10953
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10953}=\sqrt{9*1217}=\sqrt{9}*\sqrt{1217}=3\sqrt{1217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-3\sqrt{1217}}{2*12}=\frac{99-3\sqrt{1217}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+3\sqrt{1217}}{2*12}=\frac{99+3\sqrt{1217}}{24} $
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