45(33x^2+11)=768

Solution for 45(33x^2+11)=768 equation:

45(33x^2+11)=768

We move all terms to the left:

45(33x^2+11)-(768)=0

We multiply parentheses

1485x^2+495-768=0

We add all the numbers together, and all the variables

1485x^2-273=0

a = 1485; b = 0; c = -273;
Δ = b2-4ac
Δ = 02-4·1485·(-273)
Δ = 1621620
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:

$\sqrt{\Delta}=\sqrt{1621620}=\sqrt{324*5005}=\sqrt{324}*\sqrt{5005}=18\sqrt{5005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{5005}}{2*1485}=\frac{0-18\sqrt{5005}}{2970}
=-\frac{18\sqrt{5005}}{2970}
=-\frac{\sqrt{5005}}{165}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{5005}}{2*1485}=\frac{0+18\sqrt{5005}}{2970}
=\frac{18\sqrt{5005}}{2970}
=\frac{\sqrt{5005}}{165}
$