5x2-22x+11=3

Solution for 5x2-22x+11=3 equation:

5x^2-22x+11=3

We move all terms to the left:

5x^2-22x+11-(3)=0

We add all the numbers together, and all the variables

5x^2-22x+8=0

a = 5; b = -22; c = +8;
Δ = b2-4ac
Δ = -222-4·5·8
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{-(-22)-18}{2*5}=\frac{4}{10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+18}{2*5}=\frac{40}{10}
=4
$