7x2-18x+2=2x+4

Solution for 7x2-18x+2=2x+4 equation:

7x^2-18x+2=2x+4

We move all terms to the left:

7x^2-18x+2-(2x+4)=0

We get rid of parentheses

7x^2-18x-2x-4+2=0

We add all the numbers together, and all the variables

7x^2-20x-2=0

a = 7; b = -20; c = -2;
Δ = b2-4ac
Δ = -202-4·7·(-2)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{114}}{2*7}=\frac{20-2\sqrt{114}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{114}}{2*7}=\frac{20+2\sqrt{114}}{14}
$