6x^2+8=5x^2-9x

Solution for 6x^2+8=5x^2-9x equation:

6x^2+8=5x^2-9x

We move all terms to the left:

6x^2+8-(5x^2-9x)=0

We get rid of parentheses

6x^2-5x^2+9x+8=0

We add all the numbers together, and all the variables

x^2+9x+8=0

a = 1; b = 9; c = +8;
Δ = b2-4ac
Δ = 92-4·1·8
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*1}=\frac{-2}{2}
=-1
$