6(x^2)-21=-5(x^2)-4x

Solution for 6(x^2)-21=-5(x^2)-4x equation:

6(x^2)-21=-5(x^2)-4x

We move all terms to the left:

6(x^2)-21-(-5(x^2)-4x)=0

We get rid of parentheses

6x^2+5x^2+4x-21=0

We add all the numbers together, and all the variables

11x^2+4x-21=0

a = 11; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·11·(-21)
Δ = 940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{235}}{2*11}=\frac{-4-2\sqrt{235}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{235}}{2*11}=\frac{-4+2\sqrt{235}}{22}
$