(6-x)*x+x+x+(9-x)*x=15x/2

Solution for (6-x)*x+x+x+(9-x)*x=15x/2 equation:

(6-x)*x+x+x+(9-x)*x=15x/2

We move all terms to the left:

(6-x)*x+x+x+(9-x)*x-(15x/2)=0

We add all the numbers together, and all the variables

(-1x+6)*x+x+x+(-1x+9)*x-(+15x/2)=0

We add all the numbers together, and all the variables

2x+(-1x+6)*x+(-1x+9)*x-(+15x/2)=0

We multiply parentheses

-1x^2-1x^2+2x+6x+9x-(+15x/2)=0

We get rid of parentheses

-1x^2-1x^2+2x+6x+9x-15x/2=0

We multiply all the terms by the denominator


-1x^2*2-1x^2*2+2x*2+6x*2+9x*2-15x=0

We add all the numbers together, and all the variables

-1x^2*2-1x^2*2-15x+2x*2+6x*2+9x*2=0

Wy multiply elements

-2x^2-2x^2-15x+4x+12x+18x=0

We add all the numbers together, and all the variables

-4x^2+19x=0

a = -4; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-4)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-4}=\frac{-38}{-8}
=4+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-4}=\frac{0}{-8}
=0
$