7x^2+12x-22=2x+6

Solution for 7x^2+12x-22=2x+6 equation:

7x^2+12x-22=2x+6

We move all terms to the left:

7x^2+12x-22-(2x+6)=0

We get rid of parentheses

7x^2+12x-2x-6-22=0

We add all the numbers together, and all the variables

7x^2+10x-28=0

a = 7; b = 10; c = -28;
Δ = b2-4ac
Δ = 102-4·7·(-28)
Δ = 884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{221}}{2*7}=\frac{-10-2\sqrt{221}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{221}}{2*7}=\frac{-10+2\sqrt{221}}{14}
$