(4x+1)(x+6)=(x-2)(3x-4)

Solution for (4x+1)(x+6)=(x-2)(3x-4) equation:

(4x+1)(x+6)=(x-2)(3x-4)

We move all terms to the left:

(4x+1)(x+6)-((x-2)(3x-4))=0

We multiply parentheses ..

(+4x^2+24x+x+6)-((x-2)(3x-4))=0


We calculate terms in parentheses: -((x-2)(3x-4)), so:

(x-2)(3x-4)

We multiply parentheses ..

(+3x^2-4x-6x+8)

We get rid of parentheses

3x^2-4x-6x+8

We add all the numbers together, and all the variables

3x^2-10x+8

Back to the equation:

-(3x^2-10x+8)


We get rid of parentheses

4x^2-3x^2+24x+x+10x+6-8=0

We add all the numbers together, and all the variables

x^2+35x-2=0

a = 1; b = 35; c = -2;
Δ = b2-4ac
Δ = 352-4·1·(-2)
Δ = 1233
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:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-3\sqrt{137}}{2*1}=\frac{-35-3\sqrt{137}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+3\sqrt{137}}{2*1}=\frac{-35+3\sqrt{137}}{2}
$