(X-8)(x-11)=70^2

Solution for (X-8)(x-11)=70^2 equation:

(X-8)(X-11)=70^2

We move all terms to the left:

(X-8)(X-11)-(70^2)=0

We add all the numbers together, and all the variables

(X-8)(X-11)-4900=0

We multiply parentheses ..

(+X^2-11X-8X+88)-4900=0

We get rid of parentheses

X^2-11X-8X+88-4900=0

We add all the numbers together, and all the variables

X^2-19X-4812=0

a = 1; b = -19; c = -4812;
Δ = b2-4ac
Δ = -192-4·1·(-4812)
Δ = 19609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{19609}}{2*1}=\frac{19-\sqrt{19609}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{19609}}{2*1}=\frac{19+\sqrt{19609}}{2}
$