21x^2+35=-64x

Solution for 21x^2+35=-64x equation:

21x^2+35=-64x

We move all terms to the left:

21x^2+35-(-64x)=0

We get rid of parentheses

21x^2+64x+35=0

a = 21; b = 64; c = +35;
Δ = b2-4ac
Δ = 642-4·21·35
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-34}{2*21}=\frac{-98}{42}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+34}{2*21}=\frac{-30}{42}
=-5/7
$