x*x+3x=2x+22

Solution for x*x+3x=2x+22 equation:

x*x+3x=2x+22

We move all terms to the left:

x*x+3x-(2x+22)=0

We add all the numbers together, and all the variables

3x+x*x-(2x+22)=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+x-22=0

a = 1; b = 1; c = -22;
Δ = b2-4ac
Δ = 12-4·1·(-22)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{89}}{2*1}=\frac{-1-\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{89}}{2*1}=\frac{-1+\sqrt{89}}{2}
$