3(5x^2-2x^2-50)-23(7x^2+98x-2)=45

Solution for 3(5x^2-2x^2-50)-23(7x^2+98x-2)=45 equation:

3(5x^2-2x^2-50)-23(7x^2+98x-2)=45

We move all terms to the left:

3(5x^2-2x^2-50)-23(7x^2+98x-2)-(45)=0

We multiply parentheses

15x^2-6x^2-161x^2-2254x-150+46-45=0

We add all the numbers together, and all the variables

-152x^2-2254x-149=0

a = -152; b = -2254; c = -149;
Δ = b2-4ac
Δ = -22542-4·(-152)·(-149)
Δ = 4989924
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:

$\sqrt{\Delta}=\sqrt{4989924}=\sqrt{324*15401}=\sqrt{324}*\sqrt{15401}=18\sqrt{15401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2254)-18\sqrt{15401}}{2*-152}=\frac{2254-18\sqrt{15401}}{-304}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2254)+18\sqrt{15401}}{2*-152}=\frac{2254+18\sqrt{15401}}{-304}
$