4x(x-7)=-44

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Solution for 4x(x-7)=-44 equation:



4x(x-7)=-44
We move all terms to the left:
4x(x-7)-(-44)=0
We add all the numbers together, and all the variables
4x(x-7)+44=0
We multiply parentheses
4x^2-28x+44=0
a = 4; b = -28; c = +44;
Δ = b2-4ac
Δ = -282-4·4·44
Δ = 80
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:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{5}}{2*4}=\frac{28-4\sqrt{5}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{5}}{2*4}=\frac{28+4\sqrt{5}}{8} $

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