3(-5x+4)5x-1=-39

Solution for 3(-5x+4)5x-1=-39 equation:

3(-5x+4)5x-1=-39

We move all terms to the left:

3(-5x+4)5x-1-(-39)=0

We add all the numbers together, and all the variables

3(-5x+4)5x+38=0

We multiply parentheses

-75x^2+60x+38=0

a = -75; b = 60; c = +38;
Δ = b2-4ac
Δ = 602-4·(-75)·38
Δ = 15000
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:

$\sqrt{\Delta}=\sqrt{15000}=\sqrt{2500*6}=\sqrt{2500}*\sqrt{6}=50\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-50\sqrt{6}}{2*-75}=\frac{-60-50\sqrt{6}}{-150}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+50\sqrt{6}}{2*-75}=\frac{-60+50\sqrt{6}}{-150}
$