14x^2=12+13x

Solution for 14x^2=12+13x equation:

14x^2=12+13x

We move all terms to the left:

14x^2-(12+13x)=0

We add all the numbers together, and all the variables

14x^2-(13x+12)=0

We get rid of parentheses

14x^2-13x-12=0

a = 14; b = -13; c = -12;
Δ = b2-4ac
Δ = -132-4·14·(-12)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*14}=\frac{-16}{28}
=-4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*14}=\frac{42}{28}
=1+1/2
$