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3X(8X-2)=42
We move all terms to the left:
3X(8X-2)-(42)=0
We multiply parentheses
24X^2-6X-42=0
a = 24; b = -6; c = -42;
Δ = b2-4ac
Δ = -62-4·24·(-42)
Δ = 4068
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4068}=\sqrt{36*113}=\sqrt{36}*\sqrt{113}=6\sqrt{113}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{113}}{2*24}=\frac{6-6\sqrt{113}}{48} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{113}}{2*24}=\frac{6+6\sqrt{113}}{48} $
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