x2+3x+1=7x+22

Solution for x2+3x+1=7x+22 equation:

x2+3x+1=7x+22

We move all terms to the left:

x2+3x+1-(7x+22)=0

We add all the numbers together, and all the variables

x^2+3x-(7x+22)+1=0

We get rid of parentheses

x^2+3x-7x-22+1=0

We add all the numbers together, and all the variables

x^2-4x-21=0

a = 1; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*1}=\frac{14}{2}
=7
$