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(13+x)(7+x)=280
We move all terms to the left:
(13+x)(7+x)-(280)=0
We add all the numbers together, and all the variables
(x+13)(x+7)-280=0
We multiply parentheses ..
(+x^2+7x+13x+91)-280=0
We get rid of parentheses
x^2+7x+13x+91-280=0
We add all the numbers together, and all the variables
x^2+20x-189=0
a = 1; b = 20; c = -189;
Δ = b2-4ac
Δ = 202-4·1·(-189)
Δ = 1156
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1156}=34$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-34}{2*1}=\frac{-54}{2} =-27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+34}{2*1}=\frac{14}{2} =7 $
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