(x-35)(x+1)=35

Solution for (x-35)(x+1)=35 equation:

(x-35)(x+1)=35

We move all terms to the left:

(x-35)(x+1)-(35)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-34x-70=0

a = 1; b = -34; c = -70;
Δ = b2-4ac
Δ = -342-4·1·(-70)
Δ = 1436
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:

$\sqrt{\Delta}=\sqrt{1436}=\sqrt{4*359}=\sqrt{4}*\sqrt{359}=2\sqrt{359}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{359}}{2*1}=\frac{34-2\sqrt{359}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{359}}{2*1}=\frac{34+2\sqrt{359}}{2}
$