(x-40)(x+30)=97317

Solution for (x-40)(x+30)=97317 equation:

(x-40)(x+30)=97317

We move all terms to the left:

(x-40)(x+30)-(97317)=0

We multiply parentheses ..

(+x^2+30x-40x-1200)-97317=0

We get rid of parentheses

x^2+30x-40x-1200-97317=0

We add all the numbers together, and all the variables

x^2-10x-98517=0

a = 1; b = -10; c = -98517;
Δ = b2-4ac
Δ = -102-4·1·(-98517)
Δ = 394168
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:

$\sqrt{\Delta}=\sqrt{394168}=\sqrt{4*98542}=\sqrt{4}*\sqrt{98542}=2\sqrt{98542}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{98542}}{2*1}=\frac{10-2\sqrt{98542}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{98542}}{2*1}=\frac{10+2\sqrt{98542}}{2}
$