2x(x+3)+78=360

Solution for 2x(x+3)+78=360 equation:

2x(x+3)+78=360

We move all terms to the left:

2x(x+3)+78-(360)=0

We add all the numbers together, and all the variables

2x(x+3)-282=0

We multiply parentheses

2x^2+6x-282=0

a = 2; b = 6; c = -282;
Δ = b2-4ac
Δ = 62-4·2·(-282)
Δ = 2292
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:

$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{573}}{2*2}=\frac{-6-2\sqrt{573}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{573}}{2*2}=\frac{-6+2\sqrt{573}}{4}
$