(-x+15)(-x+18)=154

Solution for (-x+15)(-x+18)=154 equation:

(-x+15)(-x+18)=154

We move all terms to the left:

(-x+15)(-x+18)-(154)=0

We add all the numbers together, and all the variables

(-1x+15)(-1x+18)-154=0

We multiply parentheses ..

(+x^2-18x-15x+270)-154=0

We get rid of parentheses

x^2-18x-15x+270-154=0

We add all the numbers together, and all the variables

x^2-33x+116=0

a = 1; b = -33; c = +116;
Δ = b2-4ac
Δ = -332-4·1·116
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-25}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+25}{2*1}=\frac{58}{2}
=29
$