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4x(x+5)=44
We move all terms to the left:
4x(x+5)-(44)=0
We multiply parentheses
4x^2+20x-44=0
a = 4; b = 20; c = -44;
Δ = b2-4ac
Δ = 202-4·4·(-44)
Δ = 1104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{69}}{2*4}=\frac{-20-4\sqrt{69}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{69}}{2*4}=\frac{-20+4\sqrt{69}}{8} $
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