.825(1.6+x)(1.8-x)=2.6x+x^2

Solution for .825(1.6+x)(1.8-x)=2.6x+x^2 equation:

.825(1.6+x)(1.8-x)=2.6x+x^2

We move all terms to the left:

.825(1.6+x)(1.8-x)-(2.6x+x^2)=0

We add all the numbers together, and all the variables

-(2.6x+x^2)+.825(x+1.6)(-1x+1.8)=0

We get rid of parentheses

-x^2-2.6x+.825(x+1.6)(-1x+1.8)=0

We multiply parentheses ..

-x^2+.825(-1x^2+1.8x-1.6x+2.88)-2.6x=0

We add all the numbers together, and all the variables

-1x^2+.825(-1x^2+1.8x-1.6x+2.88)-2.6x=0

We multiply parentheses

-1x^2-0.825x^2+0.825x-0.825x-2.6x+2.376=0

We add all the numbers together, and all the variables

-1.825x^2-2.6x+2.376=0

a = -1.825; b = -2.6; c = +2.376;
Δ = b2-4ac
Δ = -2.62-4·(-1.825)·2.376
Δ = 24.1048
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{-(-2.6)-\sqrt{24.1048}}{2*-1.825}=\frac{2.6-\sqrt{24.1048}}{-3.65}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.6)+\sqrt{24.1048}}{2*-1.825}=\frac{2.6+\sqrt{24.1048}}{-3.65}
$