3(3.6-x)(0.8-x)=(1.2+x)(0.8+x)

Solution for 3(3.6-x)(0.8-x)=(1.2+x)(0.8+x) equation:

3(3.6-x)(0.8-x)=(1.2+x)(0.8+x)

We move all terms to the left:

3(3.6-x)(0.8-x)-((1.2+x)(0.8+x))=0

We add all the numbers together, and all the variables

3(-1x+3.6)(-1x+0.8)-((x+1.2)(x+0.8))=0

We multiply parentheses ..

3(+x^2-0.8x-3.6x+2.88)-((x+1.2)(x+0.8))=0


We calculate terms in parentheses: -((x+1.2)(x+0.8)), so:

(x+1.2)(x+0.8)

We multiply parentheses ..

(+x^2+0.8x+1.2x+0.96)

We get rid of parentheses

x^2+0.8x+1.2x+0.96

We add all the numbers together, and all the variables

x^2+2x+0.96

Back to the equation:

-(x^2+2x+0.96)


We multiply parentheses

3x^2+0x-9x-(x^2+2x+0.96)+8.64=0

We get rid of parentheses

3x^2-x^2+0x-9x-2x-0.96+8.64=0

We add all the numbers together, and all the variables

2x^2-10x+7.68=0

a = 2; b = -10; c = +7.68;
Δ = b2-4ac
Δ = -102-4·2·7.68
Δ = 38.56
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{-(-10)-\sqrt{38.56}}{2*2}=\frac{10-\sqrt{38.56}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{38.56}}{2*2}=\frac{10+\sqrt{38.56}}{4}
$