x(6x-29)=-28

Solution for x(6x-29)=-28 equation:

x(6x-29)=-28

We move all terms to the left:

x(6x-29)-(-28)=0

We add all the numbers together, and all the variables

x(6x-29)+28=0

We multiply parentheses

6x^2-29x+28=0

a = 6; b = -29; c = +28;
Δ = b2-4ac
Δ = -292-4·6·28
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-13}{2*6}=\frac{16}{12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+13}{2*6}=\frac{42}{12}
=3+1/2
$