(4x-3)(3x-26)=34

Solution for (4x-3)(3x-26)=34 equation:

(4x-3)(3x-26)=34

We move all terms to the left:

(4x-3)(3x-26)-(34)=0

We multiply parentheses ..

(+12x^2-104x-9x+78)-34=0

We get rid of parentheses

12x^2-104x-9x+78-34=0

We add all the numbers together, and all the variables

12x^2-113x+44=0

a = 12; b = -113; c = +44;
Δ = b2-4ac
Δ = -1132-4·12·44
Δ = 10657
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{-(-113)-\sqrt{10657}}{2*12}=\frac{113-\sqrt{10657}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-113)+\sqrt{10657}}{2*12}=\frac{113+\sqrt{10657}}{24}
$