2x(x+45.5)=116

Solution for 2x(x+45.5)=116 equation:

2x(x+45.5)=116

We move all terms to the left:

2x(x+45.5)-(116)=0

We multiply parentheses

2x^2+91x-116=0

a = 2; b = 91; c = -116;
Δ = b2-4ac
Δ = 912-4·2·(-116)
Δ = 9209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-\sqrt{9209}}{2*2}=\frac{-91-\sqrt{9209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{9209}}{2*2}=\frac{-91+\sqrt{9209}}{4}
$