2x^2+2x=7x+2

Solution for 2x^2+2x=7x+2 equation:

2x^2+2x=7x+2

We move all terms to the left:

2x^2+2x-(7x+2)=0

We get rid of parentheses

2x^2+2x-7x-2=0

We add all the numbers together, and all the variables

2x^2-5x-2=0

a = 2; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·2·(-2)
Δ = 41
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{-(-5)-\sqrt{41}}{2*2}=\frac{5-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*2}=\frac{5+\sqrt{41}}{4}
$