(3x-8)(4x-3)=6x-7

Solution for (3x-8)(4x-3)=6x-7 equation:

(3x-8)(4x-3)=6x-7

We move all terms to the left:

(3x-8)(4x-3)-(6x-7)=0

We get rid of parentheses

(3x-8)(4x-3)-6x+7=0

We multiply parentheses ..

(+12x^2-9x-32x+24)-6x+7=0

We get rid of parentheses

12x^2-9x-32x-6x+24+7=0

We add all the numbers together, and all the variables

12x^2-47x+31=0

a = 12; b = -47; c = +31;
Δ = b2-4ac
Δ = -472-4·12·31
Δ = 721
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{-(-47)-\sqrt{721}}{2*12}=\frac{47-\sqrt{721}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{721}}{2*12}=\frac{47+\sqrt{721}}{24}
$