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4x(2x+5)=-4
We move all terms to the left:
4x(2x+5)-(-4)=0
We add all the numbers together, and all the variables
4x(2x+5)+4=0
We multiply parentheses
8x^2+20x+4=0
a = 8; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·8·4
Δ = 272
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{17}}{2*8}=\frac{-20-4\sqrt{17}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{17}}{2*8}=\frac{-20+4\sqrt{17}}{16} $
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