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x(7+x)=72
We move all terms to the left:
x(7+x)-(72)=0
We add all the numbers together, and all the variables
x(x+7)-72=0
We multiply parentheses
x^2+7x-72=0
a = 1; b = 7; c = -72;
Δ = b2-4ac
Δ = 72-4·1·(-72)
Δ = 337
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{337}}{2*1}=\frac{-7-\sqrt{337}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{337}}{2*1}=\frac{-7+\sqrt{337}}{2} $
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