46=(4x+3)(3x-1)

Solution for 46=(4x+3)(3x-1) equation:

46=(4x+3)(3x-1)

We move all terms to the left:

46-((4x+3)(3x-1))=0

We multiply parentheses ..

-((+12x^2-4x+9x-3))+46=0


We calculate terms in parentheses: -((+12x^2-4x+9x-3)), so:

(+12x^2-4x+9x-3)

We get rid of parentheses

12x^2-4x+9x-3

We add all the numbers together, and all the variables

12x^2+5x-3

Back to the equation:

-(12x^2+5x-3)


We get rid of parentheses

-12x^2-5x+3+46=0

We add all the numbers together, and all the variables

-12x^2-5x+49=0

a = -12; b = -5; c = +49;
Δ = b2-4ac
Δ = -52-4·(-12)·49
Δ = 2377
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{-(-5)-\sqrt{2377}}{2*-12}=\frac{5-\sqrt{2377}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2377}}{2*-12}=\frac{5+\sqrt{2377}}{-24}
$