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(x+4)(x-6)=14
We move all terms to the left:
(x+4)(x-6)-(14)=0
We multiply parentheses ..
(+x^2-6x+4x-24)-14=0
We get rid of parentheses
x^2-6x+4x-24-14=0
We add all the numbers together, and all the variables
x^2-2x-38=0
a = 1; b = -2; c = -38;
Δ = b2-4ac
Δ = -22-4·1·(-38)
Δ = 156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{39}}{2*1}=\frac{2-2\sqrt{39}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{39}}{2*1}=\frac{2+2\sqrt{39}}{2} $
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