14x^2=29x-12

Solution for 14x^2=29x-12 equation:

14x^2=29x-12

We move all terms to the left:

14x^2-(29x-12)=0

We get rid of parentheses

14x^2-29x+12=0

a = 14; b = -29; c = +12;
Δ = b2-4ac
Δ = -292-4·14·12
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*14}=\frac{16}{28}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+13}{2*14}=\frac{42}{28}
=1+1/2
$