-8x^2-7x^2=-8+6x^2

Solution for -8x^2-7x^2=-8+6x^2 equation:

-8x^2-7x^2=-8+6x^2

We move all terms to the left:

-8x^2-7x^2-(-8+6x^2)=0

We add all the numbers together, and all the variables

-15x^2-(-8+6x^2)=0

We get rid of parentheses

-15x^2-6x^2+8=0

We add all the numbers together, and all the variables

-21x^2+8=0

a = -21; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-21)·8
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*-21}=\frac{0-4\sqrt{42}}{-42}
=-\frac{4\sqrt{42}}{-42}
=-\frac{2\sqrt{42}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*-21}=\frac{0+4\sqrt{42}}{-42}
=\frac{4\sqrt{42}}{-42}
=\frac{2\sqrt{42}}{-21}
$