116=2x(x+29)

Solution for 116=2x(x+29) equation:

116=2x(x+29)

We move all terms to the left:

116-(2x(x+29))=0


We calculate terms in parentheses: -(2x(x+29)), so:

2x(x+29)

We multiply parentheses

2x^2+58x

Back to the equation:

-(2x^2+58x)


We get rid of parentheses

-2x^2-58x+116=0

a = -2; b = -58; c = +116;
Δ = b2-4ac
Δ = -582-4·(-2)·116
Δ = 4292
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:

$\sqrt{\Delta}=\sqrt{4292}=\sqrt{4*1073}=\sqrt{4}*\sqrt{1073}=2\sqrt{1073}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{1073}}{2*-2}=\frac{58-2\sqrt{1073}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{1073}}{2*-2}=\frac{58+2\sqrt{1073}}{-4}
$