(2x-5)x-4=1

Solution for (2x-5)x-4=1 equation:

(2x-5)x-4=1

We move all terms to the left:

(2x-5)x-4-(1)=0

We add all the numbers together, and all the variables

(2x-5)x-5=0

We multiply parentheses

2x^2-5x-5=0

a = 2; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·2·(-5)
Δ = 65
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{65}}{2*2}=\frac{5-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*2}=\frac{5+\sqrt{65}}{4}
$