x.2(4x-3)-3=5x+6

Solution for x.2(4x-3)-3=5x+6 equation:

x.2(4x-3)-3=5x+6

We move all terms to the left:

x.2(4x-3)-3-(5x+6)=0

We multiply parentheses

4x^2-3x-(5x+6)-3=0

We get rid of parentheses

4x^2-3x-5x-6-3=0

We add all the numbers together, and all the variables

4x^2-8x-9=0

a = 4; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·4·(-9)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*4}=\frac{8-4\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*4}=\frac{8+4\sqrt{13}}{8}
$