0=10x-0.83x^2-13

Solution for 0=10x-0.83x^2-13 equation:

0=10x-0.83x^2-13

We move all terms to the left:

0-(10x-0.83x^2-13)=0

We add all the numbers together, and all the variables

-(10x-0.83x^2-13)=0

We get rid of parentheses

0.83x^2-10x+13=0

a = 0.83; b = -10; c = +13;
Δ = b2-4ac
Δ = -102-4·0.83·13
Δ = 56.84
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{-(-10)-\sqrt{56.84}}{2*0.83}=\frac{10-\sqrt{56.84}}{1.66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+\sqrt{56.84}}{2*0.83}=\frac{10+\sqrt{56.84}}{1.66}
$