45x^2-90x=9-18

Solution for 45x^2-90x=9-18 equation:

45x^2-90x=9-18

We move all terms to the left:

45x^2-90x-(9-18)=0

We add all the numbers together, and all the variables

45x^2-90x-(-9)=0

We add all the numbers together, and all the variables

45x^2-90x+9=0

a = 45; b = -90; c = +9;
Δ = b2-4ac
Δ = -902-4·45·9
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-36\sqrt{5}}{2*45}=\frac{90-36\sqrt{5}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+36\sqrt{5}}{2*45}=\frac{90+36\sqrt{5}}{90}
$