(x-5)(x-2)=98

Solution for (x-5)(x-2)=98 equation:

(x-5)(x-2)=98

We move all terms to the left:

(x-5)(x-2)-(98)=0

We multiply parentheses ..

(+x^2-2x-5x+10)-98=0

We get rid of parentheses

x^2-2x-5x+10-98=0

We add all the numbers together, and all the variables

x^2-7x-88=0

a = 1; b = -7; c = -88;
Δ = b2-4ac
Δ = -72-4·1·(-88)
Δ = 401
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{-(-7)-\sqrt{401}}{2*1}=\frac{7-\sqrt{401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{401}}{2*1}=\frac{7+\sqrt{401}}{2}
$