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4x(2x+3)=-2x-4
We move all terms to the left:
4x(2x+3)-(-2x-4)=0
We multiply parentheses
8x^2+12x-(-2x-4)=0
We get rid of parentheses
8x^2+12x+2x+4=0
We add all the numbers together, and all the variables
8x^2+14x+4=0
a = 8; b = 14; c = +4;
Δ = b2-4ac
Δ = 142-4·8·4
Δ = 68
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{17}}{2*8}=\frac{-14-2\sqrt{17}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{17}}{2*8}=\frac{-14+2\sqrt{17}}{16} $
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