5.2x(x-4.75)=-20.8

Solution for 5.2x(x-4.75)=-20.8 equation:

5.2x(x-4.75)=-20.8

We move all terms to the left:

5.2x(x-4.75)-(-20.8)=0

We add all the numbers together, and all the variables

5.2x(x-4.75)+20.8=0

We multiply parentheses

5x^2-23.75x+20.8=0

a = 5; b = -23.75; c = +20.8;
Δ = b2-4ac
Δ = -23.752-4·5·20.8
Δ = 148.0625
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{-(-23.75)-\sqrt{148.0625}}{2*5}=\frac{23.75-\sqrt{148.0625}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23.75)+\sqrt{148.0625}}{2*5}=\frac{23.75+\sqrt{148.0625}}{10}
$