X(8x-29)=12

Solution for X(8x-29)=12 equation:

X(8X-29)=12

We move all terms to the left:

X(8X-29)-(12)=0

We multiply parentheses

8X^2-29X-12=0

a = 8; b = -29; c = -12;
Δ = b2-4ac
Δ = -292-4·8·(-12)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-35}{2*8}=\frac{-6}{16}
=-3/8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+35}{2*8}=\frac{64}{16}
=4
$