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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-30x-(5(x+5))=0


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

5(x+5)

We multiply parentheses

5x+25

Back to the equation:

-(5x+25)


We get rid of parentheses

6x^2-30x-5x-25=0

We add all the numbers together, and all the variables

6x^2-35x-25=0

a = 6; b = -35; c = -25;
Δ = b2-4ac
Δ = -352-4·6·(-25)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{73}}{2*6}=\frac{35-5\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{73}}{2*6}=\frac{35+5\sqrt{73}}{12}
$