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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

(X+3)(2X-7)-6X+21=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2X^2-7X=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$