2x^2-5x+8=23

Solution for 2x^2-5x+8=23 equation:

2x^2-5x+8=23

We move all terms to the left:

2x^2-5x+8-(23)=0

We add all the numbers together, and all the variables

2x^2-5x-15=0

a = 2; b = -5; c = -15;
Δ = b2-4ac
Δ = -52-4·2·(-15)
Δ = 145
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{-(-5)-\sqrt{145}}{2*2}=\frac{5-\sqrt{145}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*2}=\frac{5+\sqrt{145}}{4}
$