-10x^2+6x+0.5=0

Solution for -10x^2+6x+0.5=0 equation:

-10x^2+6x+0.5=0

a = -10; b = 6; c = +0.5;
Δ = b2-4ac
Δ = 62-4·(-10)·0.5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{14}}{2*-10}=\frac{-6-2\sqrt{14}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{14}}{2*-10}=\frac{-6+2\sqrt{14}}{-20}
$