5.75x(x+5)+4.50=5.25

Solution for 5.75x(x+5)+4.50=5.25 equation:

5.75x(x+5)+4.50=5.25

We move all terms to the left:

5.75x(x+5)+4.50-(5.25)=0

We add all the numbers together, and all the variables

5.75x(x+5)-0.75=0

We multiply parentheses

5x^2+25x-0.75=0

a = 5; b = 25; c = -0.75;
Δ = b2-4ac
Δ = 252-4·5·(-0.75)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-8\sqrt{10}}{2*5}=\frac{-25-8\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+8\sqrt{10}}{2*5}=\frac{-25+8\sqrt{10}}{10}
$