3x(x+22)=-3(4x+10)

Solution for 3x(x+22)=-3(4x+10) equation:

3x(x+22)=-3(4x+10)

We move all terms to the left:

3x(x+22)-(-3(4x+10))=0

We multiply parentheses

3x^2+66x-(-3(4x+10))=0


We calculate terms in parentheses: -(-3(4x+10)), so:

-3(4x+10)

We multiply parentheses

-12x-30

Back to the equation:

-(-12x-30)


We get rid of parentheses

3x^2+66x+12x+30=0

We add all the numbers together, and all the variables

3x^2+78x+30=0

a = 3; b = 78; c = +30;
Δ = b2-4ac
Δ = 782-4·3·30
Δ = 5724
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:

$\sqrt{\Delta}=\sqrt{5724}=\sqrt{36*159}=\sqrt{36}*\sqrt{159}=6\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-6\sqrt{159}}{2*3}=\frac{-78-6\sqrt{159}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+6\sqrt{159}}{2*3}=\frac{-78+6\sqrt{159}}{6}
$