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(x+20)(x-5)=450
We move all terms to the left:
(x+20)(x-5)-(450)=0
We multiply parentheses ..
(+x^2-5x+20x-100)-450=0
We get rid of parentheses
x^2-5x+20x-100-450=0
We add all the numbers together, and all the variables
x^2+15x-550=0
a = 1; b = 15; c = -550;
Δ = b2-4ac
Δ = 152-4·1·(-550)
Δ = 2425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{97}}{2*1}=\frac{-15-5\sqrt{97}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{97}}{2*1}=\frac{-15+5\sqrt{97}}{2} $
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