4x^2+21=-3x^2+38

Solution for 4x^2+21=-3x^2+38 equation:

4x^2+21=-3x^2+38

We move all terms to the left:

4x^2+21-(-3x^2+38)=0

We get rid of parentheses

4x^2+3x^2-38+21=0

We add all the numbers together, and all the variables

7x^2-17=0

a = 7; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·7·(-17)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{119}}{2*7}=\frac{0-2\sqrt{119}}{14}
=-\frac{2\sqrt{119}}{14}
=-\frac{\sqrt{119}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{119}}{2*7}=\frac{0+2\sqrt{119}}{14}
=\frac{2\sqrt{119}}{14}
=\frac{\sqrt{119}}{7}
$