3(-2x+5)*4x=17

Solution for 3(-2x+5)*4x=17 equation:

3(-2x+5)*4x=17

We move all terms to the left:

3(-2x+5)*4x-(17)=0

We multiply parentheses

-24x^2+60x-17=0

a = -24; b = 60; c = -17;
Δ = b2-4ac
Δ = 602-4·(-24)·(-17)
Δ = 1968
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:

$\sqrt{\Delta}=\sqrt{1968}=\sqrt{16*123}=\sqrt{16}*\sqrt{123}=4\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{123}}{2*-24}=\frac{-60-4\sqrt{123}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{123}}{2*-24}=\frac{-60+4\sqrt{123}}{-48}
$