7=8+10x+20x^2

Solution for 7=8+10x+20x^2 equation:

7=8+10x+20x^2

We move all terms to the left:

7-(8+10x+20x^2)=0

We get rid of parentheses

-20x^2-10x-8+7=0

We add all the numbers together, and all the variables

-20x^2-10x-1=0

a = -20; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-20)·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*-20}=\frac{10-2\sqrt{5}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*-20}=\frac{10+2\sqrt{5}}{-40}
$