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6x+2(x-5)*4x=44
We move all terms to the left:
6x+2(x-5)*4x-(44)=0
We multiply parentheses
8x^2+6x-40x-44=0
We add all the numbers together, and all the variables
8x^2-34x-44=0
a = 8; b = -34; c = -44;
Δ = b2-4ac
Δ = -342-4·8·(-44)
Δ = 2564
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2564}=\sqrt{4*641}=\sqrt{4}*\sqrt{641}=2\sqrt{641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{641}}{2*8}=\frac{34-2\sqrt{641}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{641}}{2*8}=\frac{34+2\sqrt{641}}{16} $
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