(X-3)*(2x-7)=0

Solution for (X-3)*(2x-7)=0 equation:

(X-3)(2X-7)=0

We multiply parentheses ..

(+2X^2-7X-6X+21)=0

We get rid of parentheses

2X^2-7X-6X+21=0

We add all the numbers together, and all the variables

2X^2-13X+21=0

a = 2; b = -13; c = +21;
Δ = b2-4ac
Δ = -132-4·2·21
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-1}{2*2}=\frac{12}{4}
=3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+1}{2*2}=\frac{14}{4}
=3+1/2
$