(6-x)*x+x+x+(9-x)*x=13.5

Solution for (6-x)*x+x+x+(9-x)*x=13.5 equation:

(6-x)*x+x+x+(9-x)*x=13.5

We move all terms to the left:

(6-x)*x+x+x+(9-x)*x-(13.5)=0

We add all the numbers together, and all the variables

(-1x+6)*x+x+x+(-1x+9)*x-(13.5)=0

We add all the numbers together, and all the variables

2x+(-1x+6)*x+(-1x+9)*x-13.5=0

We multiply parentheses

-1x^2-1x^2+2x+6x+9x-13.5=0

We add all the numbers together, and all the variables

-2x^2+17x-13.5=0

a = -2; b = 17; c = -13.5;
Δ = b2-4ac
Δ = 172-4·(-2)·(-13.5)
Δ = 181
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{-(17)-\sqrt{181}}{2*-2}=\frac{-17-\sqrt{181}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{181}}{2*-2}=\frac{-17+\sqrt{181}}{-4}
$