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3x(2x+1)=8x+21
We move all terms to the left:
3x(2x+1)-(8x+21)=0
We multiply parentheses
6x^2+3x-(8x+21)=0
We get rid of parentheses
6x^2+3x-8x-21=0
We add all the numbers together, and all the variables
6x^2-5x-21=0
a = 6; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·6·(-21)
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*6}=\frac{-18}{12} =-1+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*6}=\frac{28}{12} =2+1/3 $
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