-8x2+129x-339=-5x2+84x-171

Solution for -8x2+129x-339=-5x2+84x-171 equation:

-8x^2+129x-339=-5x^2+84x-171

We move all terms to the left:

-8x^2+129x-339-(-5x^2+84x-171)=0

We get rid of parentheses

-8x^2+5x^2-84x+129x+171-339=0

We add all the numbers together, and all the variables

-3x^2+45x-168=0

a = -3; b = 45; c = -168;
Δ = b2-4ac
Δ = 452-4·(-3)·(-168)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3}{2*-3}=\frac{-48}{-6}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3}{2*-3}=\frac{-42}{-6}
=+7
$