5x^2+x-1/2=0

Solution for 5x^2+x-1/2=0 equation:

5x^2+x-1/2=0

We multiply all the terms by the denominator


5x^2*2+x*2-1=0

Wy multiply elements

10x^2+2x-1=0

a = 10; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·10·(-1)
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*10}=\frac{-2-2\sqrt{11}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*10}=\frac{-2+2\sqrt{11}}{20}
$