(54-0.9x)(4.5+1.5x)=0

Solution for (54-0.9x)(4.5+1.5x)=0 equation:

(54-0.9x)(4.5+1.5x)=0

We add all the numbers together, and all the variables

(-0.9x+54)(1.5x+4.5)=0

We multiply parentheses ..

(+0x^2+0x+54x+243)=0

We get rid of parentheses

0x^2+0x+54x+243=0

We add all the numbers together, and all the variables

x^2+55x+243=0

a = 1; b = 55; c = +243;
Δ = b2-4ac
Δ = 552-4·1·243
Δ = 2053
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{-(55)-\sqrt{2053}}{2*1}=\frac{-55-\sqrt{2053}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{2053}}{2*1}=\frac{-55+\sqrt{2053}}{2}
$