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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4x^2-3x+24x-18)-((2x+3))=0


We calculate terms in parentheses: -((2x+3)), so:

(2x+3)

We get rid of parentheses

2x+3

Back to the equation:

-(2x+3)


We get rid of parentheses

4x^2-3x+24x-2x-18-3=0

We add all the numbers together, and all the variables

4x^2+19x-21=0

a = 4; b = 19; c = -21;
Δ = b2-4ac
Δ = 192-4·4·(-21)
Δ = 697
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{697}}{2*4}=\frac{-19-\sqrt{697}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{697}}{2*4}=\frac{-19+\sqrt{697}}{8}
$