67+(3x+30)+3x(x-31)=360

Solution for 67+(3x+30)+3x(x-31)=360 equation:

67+(3x+30)+3x(x-31)=360

We move all terms to the left:

67+(3x+30)+3x(x-31)-(360)=0

We add all the numbers together, and all the variables

(3x+30)+3x(x-31)-293=0

We multiply parentheses

3x^2+(3x+30)-93x-293=0

We get rid of parentheses

3x^2+3x-93x+30-293=0

We add all the numbers together, and all the variables

3x^2-90x-263=0

a = 3; b = -90; c = -263;
Δ = b2-4ac
Δ = -902-4·3·(-263)
Δ = 11256
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:

$\sqrt{\Delta}=\sqrt{11256}=\sqrt{4*2814}=\sqrt{4}*\sqrt{2814}=2\sqrt{2814}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2814}}{2*3}=\frac{90-2\sqrt{2814}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2814}}{2*3}=\frac{90+2\sqrt{2814}}{6}
$