4x2-5x(x+6)=2x+3

Solution for 4x2-5x(x+6)=2x+3 equation:

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

We move all terms to the left:

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

We multiply parentheses

4x^2-5x^2-30x-(2x+3)=0

We get rid of parentheses

4x^2-5x^2-30x-2x-3=0

We add all the numbers together, and all the variables

-1x^2-32x-3=0

a = -1; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·(-1)·(-3)
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{253}}{2*-1}=\frac{32-2\sqrt{253}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{253}}{2*-1}=\frac{32+2\sqrt{253}}{-2}
$