x^2+308=35x+8

Solution for x^2+308=35x+8 equation:

x^2+308=35x+8

We move all terms to the left:

x^2+308-(35x+8)=0

We get rid of parentheses

x^2-35x-8+308=0

We add all the numbers together, and all the variables

x^2-35x+300=0

a = 1; b = -35; c = +300;
Δ = b2-4ac
Δ = -352-4·1·300
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5}{2*1}=\frac{30}{2}
=15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5}{2*1}=\frac{40}{2}
=20
$