X^2-x-35=5x+5

Solution for X^2-x-35=5x+5 equation:

X^2-X-35=5X+5

We move all terms to the left:

X^2-X-35-(5X+5)=0

We add all the numbers together, and all the variables

X^2-1X-(5X+5)-35=0

We get rid of parentheses

X^2-1X-5X-5-35=0

We add all the numbers together, and all the variables

X^2-6X-40=0

a = 1; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·1·(-40)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*1}=\frac{20}{2}
=10
$