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3x(6x+7)=2
We move all terms to the left:
3x(6x+7)-(2)=0
We multiply parentheses
18x^2+21x-2=0
a = 18; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·18·(-2)
Δ = 585
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*18}=\frac{-21-3\sqrt{65}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*18}=\frac{-21+3\sqrt{65}}{36} $
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