x(x+25)+(x-25)+1.5x=360

Solution for x(x+25)+(x-25)+1.5x=360 equation:

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}
$