4.5x(x-2)=-0.5+21

Solution for 4.5x(x-2)=-0.5+21 equation:

4.5x(x-2)=-0.5+21

We move all terms to the left:

4.5x(x-2)-(-0.5+21)=0

We add all the numbers together, and all the variables

4.5x(x-2)-(20.5)=0

We add all the numbers together, and all the variables

4.5x(x-2)-20.5=0

We multiply parentheses

4x^2-8x-20.5=0

a = 4; b = -8; c = -20.5;
Δ = b2-4ac
Δ = -82-4·4·(-20.5)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-14\sqrt{2}}{2*4}=\frac{8-14\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+14\sqrt{2}}{2*4}=\frac{8+14\sqrt{2}}{8}
$