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7x+3x(4x-8)=109
We move all terms to the left:
7x+3x(4x-8)-(109)=0
We multiply parentheses
12x^2+7x-24x-109=0
We add all the numbers together, and all the variables
12x^2-17x-109=0
a = 12; b = -17; c = -109;
Δ = b2-4ac
Δ = -172-4·12·(-109)
Δ = 5521
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{5521}}{2*12}=\frac{17-\sqrt{5521}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{5521}}{2*12}=\frac{17+\sqrt{5521}}{24} $
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