(5-3x)(2+6)=(3x+5)(3-x)

Solution for (5-3x)(2+6)=(3x+5)(3-x) equation:

(5-3x)(2+6)=(3x+5)(3-x)

We move all terms to the left:

(5-3x)(2+6)-((3x+5)(3-x))=0

We add all the numbers together, and all the variables

(-3x+5)8-((3x+5)(-1x+3))=0

We multiply parentheses

-24x-((3x+5)(-1x+3))+40=0

We multiply parentheses ..

-((-3x^2+9x-5x+15))-24x+40=0


We calculate terms in parentheses: -((-3x^2+9x-5x+15)), so:

(-3x^2+9x-5x+15)

We get rid of parentheses

-3x^2+9x-5x+15

We add all the numbers together, and all the variables

-3x^2+4x+15

Back to the equation:

-(-3x^2+4x+15)


We get rid of parentheses

3x^2-4x-24x-15+40=0

We add all the numbers together, and all the variables

3x^2-28x+25=0

a = 3; b = -28; c = +25;
Δ = b2-4ac
Δ = -282-4·3·25
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-22}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+22}{2*3}=\frac{50}{6}
=8+1/3
$