5x(3x-3)=30x+10(3x+6)

Solution for 5x(3x-3)=30x+10(3x+6) equation:

5x(3x-3)=30x+10(3x+6)

We move all terms to the left:

5x(3x-3)-(30x+10(3x+6))=0

We multiply parentheses

15x^2-15x-(30x+10(3x+6))=0


We calculate terms in parentheses: -(30x+10(3x+6)), so:

30x+10(3x+6)

We multiply parentheses

30x+30x+60

We add all the numbers together, and all the variables

60x+60

Back to the equation:

-(60x+60)


We get rid of parentheses

15x^2-15x-60x-60=0

We add all the numbers together, and all the variables

15x^2-75x-60=0

a = 15; b = -75; c = -60;
Δ = b2-4ac
Δ = -752-4·15·(-60)
Δ = 9225
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:

$\sqrt{\Delta}=\sqrt{9225}=\sqrt{225*41}=\sqrt{225}*\sqrt{41}=15\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-15\sqrt{41}}{2*15}=\frac{75-15\sqrt{41}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+15\sqrt{41}}{2*15}=\frac{75+15\sqrt{41}}{30}
$