x.2(x+4.5)=32

Solution for x.2(x+4.5)=32 equation:

x.2(x+4.5)=32

We move all terms to the left:

x.2(x+4.5)-(32)=0

We multiply parentheses

x^2+4.5x-32=0

a = 1; b = 4.5; c = -32;
Δ = b2-4ac
Δ = 4.52-4·1·(-32)
Δ = 148.25
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{-(4.5)-\sqrt{148.25}}{2*1}=\frac{-4.5-\sqrt{148.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{148.25}}{2*1}=\frac{-4.5+\sqrt{148.25}}{2}
$