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x(x+25)+(x-25)+1.5x=360
We move all terms to the left:
x(x+25)+(x-25)+1.5x-(360)=0
We add all the numbers together, and all the variables
1.5x+x(x+25)+(x-25)-360=0
We multiply parentheses
x^2+1.5x+25x+(x-25)-360=0
We get rid of parentheses
x^2+1.5x+25x+x-25-360=0
We add all the numbers together, and all the variables
x^2+27.5x-385=0
a = 1; b = 27.5; c = -385;
Δ = b2-4ac
Δ = 27.52-4·1·(-385)
Δ = 2296.25
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{-(27.5)-\sqrt{2296.25}}{2*1}=\frac{-27.5-\sqrt{2296.25}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27.5)+\sqrt{2296.25}}{2*1}=\frac{-27.5+\sqrt{2296.25}}{2} $
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