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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(x+5)

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)


We get rid of parentheses

3x^2-15x-2x-10=0

We add all the numbers together, and all the variables

3x^2-17x-10=0

a = 3; b = -17; c = -10;
Δ = b2-4ac
Δ = -172-4·3·(-10)
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{409}}{2*3}=\frac{17-\sqrt{409}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{409}}{2*3}=\frac{17+\sqrt{409}}{6}
$