(3x+5)+(4x-1)=(2x+3)*(6x-1)

Solution for (3x+5)+(4x-1)=(2x+3)*(6x-1) equation:

(3x+5)+(4x-1)=(2x+3)(6x-1)

We move all terms to the left:

(3x+5)+(4x-1)-((2x+3)(6x-1))=0

We get rid of parentheses

3x+4x-((2x+3)(6x-1))+5-1=0

We multiply parentheses ..

-((+12x^2-2x+18x-3))+3x+4x+5-1=0


We calculate terms in parentheses: -((+12x^2-2x+18x-3)), so:

(+12x^2-2x+18x-3)

We get rid of parentheses

12x^2-2x+18x-3

We add all the numbers together, and all the variables

12x^2+16x-3

Back to the equation:

-(12x^2+16x-3)


We add all the numbers together, and all the variables

7x-(12x^2+16x-3)+4=0

We get rid of parentheses

-12x^2+7x-16x+3+4=0

We add all the numbers together, and all the variables

-12x^2-9x+7=0

a = -12; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·(-12)·7
Δ = 417
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{-(-9)-\sqrt{417}}{2*-12}=\frac{9-\sqrt{417}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{417}}{2*-12}=\frac{9+\sqrt{417}}{-24}
$