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(2x+6)(x-4)=69
We move all terms to the left:
(2x+6)(x-4)-(69)=0
We multiply parentheses ..
(+2x^2-8x+6x-24)-69=0
We get rid of parentheses
2x^2-8x+6x-24-69=0
We add all the numbers together, and all the variables
2x^2-2x-93=0
a = 2; b = -2; c = -93;
Δ = b2-4ac
Δ = -22-4·2·(-93)
Δ = 748
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{187}}{2*2}=\frac{2-2\sqrt{187}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{187}}{2*2}=\frac{2+2\sqrt{187}}{4} $
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