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5x(3x+1)=6x+2
We move all terms to the left:
5x(3x+1)-(6x+2)=0
We multiply parentheses
15x^2+5x-(6x+2)=0
We get rid of parentheses
15x^2+5x-6x-2=0
We add all the numbers together, and all the variables
15x^2-1x-2=0
a = 15; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·15·(-2)
Δ = 121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*15}=\frac{-10}{30} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*15}=\frac{12}{30} =2/5 $
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