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2x(3x+5)=4x+6
We move all terms to the left:
2x(3x+5)-(4x+6)=0
We multiply parentheses
6x^2+10x-(4x+6)=0
We get rid of parentheses
6x^2+10x-4x-6=0
We add all the numbers together, and all the variables
6x^2+6x-6=0
a = 6; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·6·(-6)
Δ = 180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{5}}{2*6}=\frac{-6-6\sqrt{5}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{5}}{2*6}=\frac{-6+6\sqrt{5}}{12} $
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