5x(x-3)-3x=8x-15-6x

Solution for 5x(x-3)-3x=8x-15-6x equation:

5x(x-3)-3x=8x-15-6x

We move all terms to the left:

5x(x-3)-3x-(8x-15-6x)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

5x^2-3x-15x-2x+15=0

We add all the numbers together, and all the variables

5x^2-20x+15=0

a = 5; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·5·15
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*5}=\frac{30}{10}
=3
$