Y=6x+4x-3x-2x+8x^2-5

Solution for Y=6x+4x-3x-2x+8x^2-5 equation:

=6Y+4Y-3Y-2Y+8Y^2-5

We move all terms to the left:

-(6Y+4Y-3Y-2Y+8Y^2-5)=0

We get rid of parentheses

-8Y^2-6Y-4Y+3Y+2Y+5=0

We add all the numbers together, and all the variables

-8Y^2-5Y+5=0

a = -8; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-8)·5
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{185}}{2*-8}=\frac{5-\sqrt{185}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{185}}{2*-8}=\frac{5+\sqrt{185}}{-16}
$