(x-4)(2x-3)=121

Solution for (x-4)(2x-3)=121 equation:

(x-4)(2x-3)=121

We move all terms to the left:

(x-4)(2x-3)-(121)=0

We multiply parentheses ..

(+2x^2-3x-8x+12)-121=0

We get rid of parentheses

2x^2-3x-8x+12-121=0

We add all the numbers together, and all the variables

2x^2-11x-109=0

a = 2; b = -11; c = -109;
Δ = b2-4ac
Δ = -112-4·2·(-109)
Δ = 993
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{-(-11)-\sqrt{993}}{2*2}=\frac{11-\sqrt{993}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{993}}{2*2}=\frac{11+\sqrt{993}}{4}
$