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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

-((-14x^2+10x-21x+15))+2x+3x+3-7=0


We calculate terms in parentheses: -((-14x^2+10x-21x+15)), so:

(-14x^2+10x-21x+15)

We get rid of parentheses

-14x^2+10x-21x+15

We add all the numbers together, and all the variables

-14x^2-11x+15

Back to the equation:

-(-14x^2-11x+15)


We add all the numbers together, and all the variables

-(-14x^2-11x+15)+5x-4=0

We get rid of parentheses

14x^2+11x+5x-15-4=0

We add all the numbers together, and all the variables

14x^2+16x-19=0

a = 14; b = 16; c = -19;
Δ = b2-4ac
Δ = 162-4·14·(-19)
Δ = 1320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{330}}{2*14}=\frac{-16-2\sqrt{330}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{330}}{2*14}=\frac{-16+2\sqrt{330}}{28}
$