(3x-1)(2x-5)=36x-29

Solution for (3x-1)(2x-5)=36x-29 equation:

(3x-1)(2x-5)=36x-29

We move all terms to the left:

(3x-1)(2x-5)-(36x-29)=0

We get rid of parentheses

(3x-1)(2x-5)-36x+29=0

We multiply parentheses ..

(+6x^2-15x-2x+5)-36x+29=0

We get rid of parentheses

6x^2-15x-2x-36x+5+29=0

We add all the numbers together, and all the variables

6x^2-53x+34=0

a = 6; b = -53; c = +34;
Δ = b2-4ac
Δ = -532-4·6·34
Δ = 1993
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{-(-53)-\sqrt{1993}}{2*6}=\frac{53-\sqrt{1993}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{1993}}{2*6}=\frac{53+\sqrt{1993}}{12}
$