4x(x-4)=3x-9

Solution for 4x(x-4)=3x-9 equation:

4x(x-4)=3x-9

We move all terms to the left:

4x(x-4)-(3x-9)=0

We multiply parentheses

4x^2-16x-(3x-9)=0

We get rid of parentheses

4x^2-16x-3x+9=0

We add all the numbers together, and all the variables

4x^2-19x+9=0

a = 4; b = -19; c = +9;
Δ = b2-4ac
Δ = -192-4·4·9
Δ = 217
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{-(-19)-\sqrt{217}}{2*4}=\frac{19-\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{217}}{2*4}=\frac{19+\sqrt{217}}{8}
$