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

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

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

We move all terms to the left:

6x^2-9x-(5x^2-8)=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{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*1}=\frac{16}{2}
=8
$