x(4.25+x)=124.5

Solution for x(4.25+x)=124.5 equation:

x(4.25+x)=124.5

We move all terms to the left:

x(4.25+x)-(124.5)=0

We add all the numbers together, and all the variables

x(x+4.25)-(124.5)=0

We add all the numbers together, and all the variables

x(x+4.25)-124.5=0

We multiply parentheses

x^2+4.25x-124.5=0

a = 1; b = 4.25; c = -124.5;
Δ = b2-4ac
Δ = 4.252-4·1·(-124.5)
Δ = 516.0625
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{-(4.25)-\sqrt{516.0625}}{2*1}=\frac{-4.25-\sqrt{516.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.25)+\sqrt{516.0625}}{2*1}=\frac{-4.25+\sqrt{516.0625}}{2}
$