(2x+3)(x-7)=4(x+7)

Solution for (2x+3)(x-7)=4(x+7) equation:

(2x+3)(x-7)=4(x+7)

We move all terms to the left:

(2x+3)(x-7)-(4(x+7))=0

We multiply parentheses ..

(+2x^2-14x+3x-21)-(4(x+7))=0


We calculate terms in parentheses: -(4(x+7)), so:

4(x+7)

We multiply parentheses

4x+28

Back to the equation:

-(4x+28)


We get rid of parentheses

2x^2-14x+3x-4x-21-28=0

We add all the numbers together, and all the variables

2x^2-15x-49=0

a = 2; b = -15; c = -49;
Δ = b2-4ac
Δ = -152-4·2·(-49)
Δ = 617
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{-(-15)-\sqrt{617}}{2*2}=\frac{15-\sqrt{617}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{617}}{2*2}=\frac{15+\sqrt{617}}{4}
$