x(2x+10)=408

Solution for x(2x+10)=408 equation:

x(2x+10)=408

We move all terms to the left:

x(2x+10)-(408)=0

We multiply parentheses

2x^2+10x-408=0

a = 2; b = 10; c = -408;
Δ = b2-4ac
Δ = 102-4·2·(-408)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-58}{2*2}=\frac{-68}{4}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+58}{2*2}=\frac{48}{4}
=12
$