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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(5x(5x+3)-2x)+15=0


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

5x(5x+3)-2x

We add all the numbers together, and all the variables

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

We multiply parentheses

25x^2-2x+15x

We add all the numbers together, and all the variables

25x^2+13x

Back to the equation:

-(25x^2+13x)


We get rid of parentheses

-25x^2+3x-13x+15=0

We add all the numbers together, and all the variables

-25x^2-10x+15=0

a = -25; b = -10; c = +15;
Δ = b2-4ac
Δ = -102-4·(-25)·15
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-40}{2*-25}=\frac{-30}{-50}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+40}{2*-25}=\frac{50}{-50}
=-1
$