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6x(3x-1)=2x+3
We move all terms to the left:
6x(3x-1)-(2x+3)=0
We multiply parentheses
18x^2-6x-(2x+3)=0
We get rid of parentheses
18x^2-6x-2x-3=0
We add all the numbers together, and all the variables
18x^2-8x-3=0
a = 18; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·18·(-3)
Δ = 280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{70}}{2*18}=\frac{8-2\sqrt{70}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{70}}{2*18}=\frac{8+2\sqrt{70}}{36} $
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