1+5x+6x2=22

Solution for 1+5x+6x2=22 equation:

1+5x+6x^2=22

We move all terms to the left:

1+5x+6x^2-(22)=0

We add all the numbers together, and all the variables

6x^2+5x-21=0

a = 6; b = 5; c = -21;
Δ = b2-4ac
Δ = 52-4·6·(-21)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-23}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+23}{2*6}=\frac{18}{12}
=1+1/2
$