(x-7)(x)=154

Solution for (x-7)(x)=154 equation:

(x-7)(x)=154

We move all terms to the left:

(x-7)(x)-(154)=0

We multiply parentheses

x^2-7x-154=0

a = 1; b = -7; c = -154;
Δ = b2-4ac
Δ = -72-4·1·(-154)
Δ = 665
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{665}}{2*1}=\frac{7-\sqrt{665}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{665}}{2*1}=\frac{7+\sqrt{665}}{2}
$