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

Solution for 3x(x-5)=-5(x+1) equation:

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

We move all terms to the left:

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

We multiply parentheses

3x^2-15x-(-5(x+1))=0


We calculate terms in parentheses: -(-5(x+1)), so:

-5(x+1)

We multiply parentheses

-5x-5

Back to the equation:

-(-5x-5)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-10x+5=0

a = 3; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·3·5
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{10}}{2*3}=\frac{10-2\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{10}}{2*3}=\frac{10+2\sqrt{10}}{6}
$