4x(2x-9)=3x+4

Solution for 4x(2x-9)=3x+4 equation:

4x(2x-9)=3x+4

We move all terms to the left:

4x(2x-9)-(3x+4)=0

We multiply parentheses

8x^2-36x-(3x+4)=0

We get rid of parentheses

8x^2-36x-3x-4=0

We add all the numbers together, and all the variables

8x^2-39x-4=0

a = 8; b = -39; c = -4;
Δ = b2-4ac
Δ = -392-4·8·(-4)
Δ = 1649
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{-(-39)-\sqrt{1649}}{2*8}=\frac{39-\sqrt{1649}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1649}}{2*8}=\frac{39+\sqrt{1649}}{16}
$