6.76=1.8x+x^2

Solution for 6.76=1.8x+x^2 equation:

6.76=1.8x+x^2

We move all terms to the left:

6.76-(1.8x+x^2)=0

We get rid of parentheses

-x^2-1.8x+6.76=0

We add all the numbers together, and all the variables

-1x^2-1.8x+6.76=0

a = -1; b = -1.8; c = +6.76;
Δ = b2-4ac
Δ = -1.82-4·(-1)·6.76
Δ = 30.28
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{-(-1.8)-\sqrt{30.28}}{2*-1}=\frac{1.8-\sqrt{30.28}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{30.28}}{2*-1}=\frac{1.8+\sqrt{30.28}}{-2}
$