90x^2-132x+51=3

Solution for 90x^2-132x+51=3 equation:

90x^2-132x+51=3

We move all terms to the left:

90x^2-132x+51-(3)=0

We add all the numbers together, and all the variables

90x^2-132x+48=0

a = 90; b = -132; c = +48;
Δ = b2-4ac
Δ = -1322-4·90·48
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-12}{2*90}=\frac{120}{180}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+12}{2*90}=\frac{144}{180}
=4/5
$