6x^2-21=-5x

Solution for 6x^2-21=-5x equation:

6x^2-21=-5x

We move all terms to the left:

6x^2-21-(-5x)=0

We get rid of parentheses

6x^2+5x-21=0

a = 6; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·6·(-21)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*6}=\frac{18}{12}
=1+1/2
$