3(5^2x+4)=75

Solution for 3(5^2x+4)=75 equation:

3(5^2x+4)=75

We move all terms to the left:

3(5^2x+4)-(75)=0

We multiply parentheses

15x^2+12-75=0

We add all the numbers together, and all the variables

15x^2-63=0

a = 15; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·15·(-63)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{105}}{2*15}=\frac{0-6\sqrt{105}}{30}
=-\frac{6\sqrt{105}}{30}
=-\frac{\sqrt{105}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{105}}{2*15}=\frac{0+6\sqrt{105}}{30}
=\frac{6\sqrt{105}}{30}
=\frac{\sqrt{105}}{5}
$