2x^2+5x-1=4

Solution for 2x^2+5x-1=4 equation:

2x^2+5x-1=4

We move all terms to the left:

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

We add all the numbers together, and all the variables

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}
$