x(x+7.73)=127.49

Solution for x(x+7.73)=127.49 equation:

x(x+7.73)=127.49

We move all terms to the left:

x(x+7.73)-(127.49)=0

We add all the numbers together, and all the variables

x(x+7.73)-127.49=0

We multiply parentheses

x^2+7.73x-127.49=0

a = 1; b = 7.73; c = -127.49;
Δ = b2-4ac
Δ = 7.732-4·1·(-127.49)
Δ = 569.7129
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{-(7.73)-\sqrt{569.7129}}{2*1}=\frac{-7.73-\sqrt{569.7129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.73)+\sqrt{569.7129}}{2*1}=\frac{-7.73+\sqrt{569.7129}}{2}
$