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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-8x-9x+15-4=0

We add all the numbers together, and all the variables

2x^2-17x+11=0

a = 2; b = -17; c = +11;
Δ = b2-4ac
Δ = -172-4·2·11
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{201}}{2*2}=\frac{17-\sqrt{201}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{201}}{2*2}=\frac{17+\sqrt{201}}{4}
$