6x^2=-17x

Solution for 6x^2=-17x equation:

6x^2=-17x

We move all terms to the left:

6x^2-(-17x)=0

We get rid of parentheses

6x^2+17x=0

a = 6; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·6·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*6}=\frac{-34}{12}
=-2+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*6}=\frac{0}{12}
=0
$