2x^2-9x+5=6

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

2x^2-9x+5=6

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2-9x-1=0

a = 2; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·2·(-1)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{89}}{2*2}=\frac{9-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{89}}{2*2}=\frac{9+\sqrt{89}}{4}
$