3(5^2x-3)=1866

Solution for 3(5^2x-3)=1866 equation:

3(5^2x-3)=1866

We move all terms to the left:

3(5^2x-3)-(1866)=0

We multiply parentheses

15x^2-9-1866=0

We add all the numbers together, and all the variables

15x^2-1875=0

a = 15; b = 0; c = -1875;
Δ = b2-4ac
Δ = 02-4·15·(-1875)
Δ = 112500
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:

$\sqrt{\Delta}=\sqrt{112500}=\sqrt{22500*5}=\sqrt{22500}*\sqrt{5}=150\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{5}}{2*15}=\frac{0-150\sqrt{5}}{30}
=-\frac{150\sqrt{5}}{30}
=-5\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{5}}{2*15}=\frac{0+150\sqrt{5}}{30}
=\frac{150\sqrt{5}}{30}
=5\sqrt{5}
$