(8x-21)(23x-16)=29

Solution for (8x-21)(23x-16)=29 equation:

(8x-21)(23x-16)=29

We move all terms to the left:

(8x-21)(23x-16)-(29)=0

We multiply parentheses ..

(+184x^2-128x-483x+336)-29=0

We get rid of parentheses

184x^2-128x-483x+336-29=0

We add all the numbers together, and all the variables

184x^2-611x+307=0

a = 184; b = -611; c = +307;
Δ = b2-4ac
Δ = -6112-4·184·307
Δ = 147369
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{-(-611)-\sqrt{147369}}{2*184}=\frac{611-\sqrt{147369}}{368}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-611)+\sqrt{147369}}{2*184}=\frac{611+\sqrt{147369}}{368}
$