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