3.6(7.5-x)+3.6(7.5+x)=(7.5-x)(7.5+x)

Solution for 3.6(7.5-x)+3.6(7.5+x)=(7.5-x)(7.5+x) equation:

3.6(7.5-x)+3.6(7.5+x)=(7.5-x)(7.5+x)

We move all terms to the left:

3.6(7.5-x)+3.6(7.5+x)-((7.5-x)(7.5+x))=0

We add all the numbers together, and all the variables

3.6(-1x+7.5)+3.6(x+7.5)-((-1x+7.5)(x+7.5))=0

We multiply parentheses

-3.6x+3.6x-((-1x+7.5)(x+7.5))+27+27=0

We multiply parentheses ..

-((-1x^2-7.5x+7.5x+56.25))-3.6x+3.6x+27+27=0


We calculate terms in parentheses: -((-1x^2-7.5x+7.5x+56.25)), so:

(-1x^2-7.5x+7.5x+56.25)

We get rid of parentheses

-1x^2-7.5x+7.5x+56.25

We add all the numbers together, and all the variables

-1x^2+56.25

Back to the equation:

-(-1x^2+56.25)


We add all the numbers together, and all the variables

-(-1x^2+56.25)+54=0

We get rid of parentheses

1x^2-56.25+54=0

We add all the numbers together, and all the variables

x^2-2.25=0

a = 1; b = 0; c = -2.25;
Δ = b2-4ac
Δ = 02-4·1·(-2.25)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3}{2*1}=\frac{-3}{2}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3}{2*1}=\frac{3}{2}
=1+1/2
$