14x^2=29x+15

Solution for 14x^2=29x+15 equation:

14x^2=29x+15

We move all terms to the left:

14x^2-(29x+15)=0

We get rid of parentheses

14x^2-29x-15=0

a = 14; b = -29; c = -15;
Δ = b2-4ac
Δ = -292-4·14·(-15)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-41}{2*14}=\frac{-12}{28}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+41}{2*14}=\frac{70}{28}
=2+1/2
$