(-3x+7)(-x+15)=0

Solution for (-3x+7)(-x+15)=0 equation:

(-3x+7)(-x+15)=0

We add all the numbers together, and all the variables

(-3x+7)(-1x+15)=0

We multiply parentheses ..

(+3x^2-45x-7x+105)=0

We get rid of parentheses

3x^2-45x-7x+105=0

We add all the numbers together, and all the variables

3x^2-52x+105=0

a = 3; b = -52; c = +105;
Δ = b2-4ac
Δ = -522-4·3·105
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-38}{2*3}=\frac{14}{6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+38}{2*3}=\frac{90}{6}
=15
$