10x2-5x+11=9x2+x+83

Solution for 10x2-5x+11=9x2+x+83 equation:

10x^2-5x+11=9x^2+x+83

We move all terms to the left:

10x^2-5x+11-(9x^2+x+83)=0

We get rid of parentheses

10x^2-9x^2-5x-x-83+11=0

We add all the numbers together, and all the variables

x^2-6x-72=0

a = 1; b = -6; c = -72;
Δ = b2-4ac
Δ = -62-4·1·(-72)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*1}=\frac{24}{2}
=12
$