2176-55x2=1866+70x

Solution for 2176-55x2=1866+70x equation:

2176-55x^2=1866+70x

We move all terms to the left:

2176-55x^2-(1866+70x)=0

We add all the numbers together, and all the variables

-55x^2-(70x+1866)+2176=0

We get rid of parentheses

-55x^2-70x-1866+2176=0

We add all the numbers together, and all the variables

-55x^2-70x+310=0

a = -55; b = -70; c = +310;
Δ = b2-4ac
Δ = -702-4·(-55)·310
Δ = 73100
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:

$\sqrt{\Delta}=\sqrt{73100}=\sqrt{100*731}=\sqrt{100}*\sqrt{731}=10\sqrt{731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{731}}{2*-55}=\frac{70-10\sqrt{731}}{-110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{731}}{2*-55}=\frac{70+10\sqrt{731}}{-110}
$