2x(8-3x)=4x-34

Solution for 2x(8-3x)=4x-34 equation:

2x(8-3x)=4x-34

We move all terms to the left:

2x(8-3x)-(4x-34)=0

We add all the numbers together, and all the variables

2x(-3x+8)-(4x-34)=0

We multiply parentheses

-6x^2+16x-(4x-34)=0

We get rid of parentheses

-6x^2+16x-4x+34=0

We add all the numbers together, and all the variables

-6x^2+12x+34=0

a = -6; b = 12; c = +34;
Δ = b2-4ac
Δ = 122-4·(-6)·34
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{15}}{2*-6}=\frac{-12-8\sqrt{15}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{15}}{2*-6}=\frac{-12+8\sqrt{15}}{-12}
$