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x(x+45)=27(27+50)
We move all terms to the left:
x(x+45)-(27(27+50))=0
We add all the numbers together, and all the variables
x(x+45)-(2777)=0
We add all the numbers together, and all the variables
x(x+45)-2777=0
We multiply parentheses
x^2+45x-2777=0
a = 1; b = 45; c = -2777;
Δ = b2-4ac
Δ = 452-4·1·(-2777)
Δ = 13133
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{-(45)-\sqrt{13133}}{2*1}=\frac{-45-\sqrt{13133}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{13133}}{2*1}=\frac{-45+\sqrt{13133}}{2} $
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