5x^2-6=-29x

Solution for 5x^2-6=-29x equation:

5x^2-6=-29x

We move all terms to the left:

5x^2-6-(-29x)=0

We get rid of parentheses

5x^2+29x-6=0

a = 5; b = 29; c = -6;
Δ = b2-4ac
Δ = 292-4·5·(-6)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-31}{2*5}=\frac{-60}{10}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+31}{2*5}=\frac{2}{10}
=1/5
$