6x^2-29=3x+13x+8x^2

Solution for 6x^2-29=3x+13x+8x^2 equation:

6x^2-29=3x+13x+8x^2

We move all terms to the left:

6x^2-29-(3x+13x+8x^2)=0

We get rid of parentheses

6x^2-8x^2-3x-13x-29=0

We add all the numbers together, and all the variables

-2x^2-16x-29=0

a = -2; b = -16; c = -29;
Δ = b2-4ac
Δ = -162-4·(-2)·(-29)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{6}}{2*-2}=\frac{16-2\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{6}}{2*-2}=\frac{16+2\sqrt{6}}{-4}
$