3(1+4n-2)(5n-3)=25

Solution for 3(1+4n-2)(5n-3)=25 equation:

3(1+4n-2)(5n-3)=25

We move all terms to the left:

3(1+4n-2)(5n-3)-(25)=0

We add all the numbers together, and all the variables

3(4n-1)(5n-3)-25=0

We multiply parentheses ..

3(+20n^2-12n-5n+3)-25=0

We multiply parentheses

60n^2-36n-15n+9-25=0

We add all the numbers together, and all the variables

60n^2-51n-16=0

a = 60; b = -51; c = -16;
Δ = b2-4ac
Δ = -512-4·60·(-16)
Δ = 6441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{6441}}{2*60}=\frac{51-\sqrt{6441}}{120}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{6441}}{2*60}=\frac{51+\sqrt{6441}}{120}
$