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(x-4)(x+20)=69
We move all terms to the left:
(x-4)(x+20)-(69)=0
We multiply parentheses ..
(+x^2+20x-4x-80)-69=0
We get rid of parentheses
x^2+20x-4x-80-69=0
We add all the numbers together, and all the variables
x^2+16x-149=0
a = 1; b = 16; c = -149;
Δ = b2-4ac
Δ = 162-4·1·(-149)
Δ = 852
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{213}}{2*1}=\frac{-16-2\sqrt{213}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{213}}{2*1}=\frac{-16+2\sqrt{213}}{2} $
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