x^2+6x=8x+35x2+6x=8x+35

Solution for x^2+6x=8x+35x2+6x=8x+35 equation:

x^2+6x=8x+35x^2+6x=8x+35

We move all terms to the left:

x^2+6x-(8x+35x^2+6x)=0

We get rid of parentheses

x^2-35x^2-8x-6x+6x=0

We add all the numbers together, and all the variables

-34x^2-8x=0

a = -34; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-34)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-34}=\frac{0}{-68}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-34}=\frac{16}{-68}
=-4/17
$