10x^2+6x+1/2=0

Solution for 10x^2+6x+1/2=0 equation:

10x^2+6x+1/2=0

We multiply all the terms by the denominator


10x^2*2+6x*2+1=0

Wy multiply elements

20x^2+12x+1=0

a = 20; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·20·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*20}=\frac{-20}{40}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*20}=\frac{-4}{40}
=-1/10
$