6=-10x^2+8x+13

Solution for 6=-10x^2+8x+13 equation:

6=-10x^2+8x+13

We move all terms to the left:

6-(-10x^2+8x+13)=0

We get rid of parentheses

10x^2-8x-13+6=0

We add all the numbers together, and all the variables

10x^2-8x-7=0

a = 10; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·10·(-7)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{86}}{2*10}=\frac{8-2\sqrt{86}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{86}}{2*10}=\frac{8+2\sqrt{86}}{20}
$