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

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

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

We move all terms to the left:

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

We multiply parentheses

15x-(6x(x+10))+30+10=0


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

6x(x+10)

We multiply parentheses

6x^2+60x

Back to the equation:

-(6x^2+60x)


We add all the numbers together, and all the variables

15x-(6x^2+60x)+40=0

We get rid of parentheses

-6x^2+15x-60x+40=0

We add all the numbers together, and all the variables

-6x^2-45x+40=0

a = -6; b = -45; c = +40;
Δ = b2-4ac
Δ = -452-4·(-6)·40
Δ = 2985
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{-(-45)-\sqrt{2985}}{2*-6}=\frac{45-\sqrt{2985}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2985}}{2*-6}=\frac{45+\sqrt{2985}}{-12}
$