(X-7)(3x+5)=(x+7)(2x+3)

Solution for (X-7)(3x+5)=(x+7)(2x+3) equation:

(X-7)(3X+5)=(X+7)(2X+3)

We move all terms to the left:

(X-7)(3X+5)-((X+7)(2X+3))=0

We multiply parentheses ..

(+3X^2+5X-21X-35)-((X+7)(2X+3))=0


We calculate terms in parentheses: -((X+7)(2X+3)), so:

(X+7)(2X+3)

We multiply parentheses ..

(+2X^2+3X+14X+21)

We get rid of parentheses

2X^2+3X+14X+21

We add all the numbers together, and all the variables

2X^2+17X+21

Back to the equation:

-(2X^2+17X+21)


We get rid of parentheses

3X^2-2X^2+5X-21X-17X-35-21=0

We add all the numbers together, and all the variables

X^2-33X-56=0

a = 1; b = -33; c = -56;
Δ = b2-4ac
Δ = -332-4·1·(-56)
Δ = 1313
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{-(-33)-\sqrt{1313}}{2*1}=\frac{33-\sqrt{1313}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{1313}}{2*1}=\frac{33+\sqrt{1313}}{2}
$