x(2x+2)=154

Solution for x(2x+2)=154 equation:

x(2x+2)=154

We move all terms to the left:

x(2x+2)-(154)=0

We multiply parentheses

2x^2+2x-154=0

a = 2; b = 2; c = -154;
Δ = b2-4ac
Δ = 22-4·2·(-154)
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{309}}{2*2}=\frac{-2-2\sqrt{309}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{309}}{2*2}=\frac{-2+2\sqrt{309}}{4}
$