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x(11.25+x)=25
We move all terms to the left:
x(11.25+x)-(25)=0
We add all the numbers together, and all the variables
x(x+11.25)-25=0
We multiply parentheses
x^2+11.25x-25=0
a = 1; b = 11.25; c = -25;
Δ = b2-4ac
Δ = 11.252-4·1·(-25)
Δ = 226.5625
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{-(11.25)-\sqrt{226.5625}}{2*1}=\frac{-11.25-\sqrt{226.5625}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11.25)+\sqrt{226.5625}}{2*1}=\frac{-11.25+\sqrt{226.5625}}{2} $
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