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4x(x+9)+2x=32
We move all terms to the left:
4x(x+9)+2x-(32)=0
We add all the numbers together, and all the variables
2x+4x(x+9)-32=0
We multiply parentheses
4x^2+2x+36x-32=0
We add all the numbers together, and all the variables
4x^2+38x-32=0
a = 4; b = 38; c = -32;
Δ = b2-4ac
Δ = 382-4·4·(-32)
Δ = 1956
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{489}}{2*4}=\frac{-38-2\sqrt{489}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{489}}{2*4}=\frac{-38+2\sqrt{489}}{8} $
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