(4x-1)(3x=7)

Solution for (4x-1)(3x=7) equation:

(4x-1)(3x=7)

We move all terms to the left:

(4x-1)(3x-(7))=0

We multiply parentheses ..

(+12x^2-28x-3x+7)=0

We get rid of parentheses

12x^2-28x-3x+7=0

We add all the numbers together, and all the variables

12x^2-31x+7=0

a = 12; b = -31; c = +7;
Δ = b2-4ac
Δ = -312-4·12·7
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-25}{2*12}=\frac{6}{24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+25}{2*12}=\frac{56}{24}
=2+1/3
$