10x^2+11x+1=-10x^2+2x+19

Solution for 10x^2+11x+1=-10x^2+2x+19 equation:

10x^2+11x+1=-10x^2+2x+19

We move all terms to the left:

10x^2+11x+1-(-10x^2+2x+19)=0

We get rid of parentheses

10x^2+10x^2-2x+11x-19+1=0

We add all the numbers together, and all the variables

20x^2+9x-18=0

a = 20; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·20·(-18)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*20}=\frac{-48}{40}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*20}=\frac{30}{40}
=3/4
$