(2x+4)(x-7)=2(5x-3)

Solution for (2x+4)(x-7)=2(5x-3) equation:

(2x+4)(x-7)=2(5x-3)

We move all terms to the left:

(2x+4)(x-7)-(2(5x-3))=0

We multiply parentheses ..

(+2x^2-14x+4x-28)-(2(5x-3))=0


We calculate terms in parentheses: -(2(5x-3)), so:

2(5x-3)

We multiply parentheses

10x-6

Back to the equation:

-(10x-6)


We get rid of parentheses

2x^2-14x+4x-10x-28+6=0

We add all the numbers together, and all the variables

2x^2-20x-22=0

a = 2; b = -20; c = -22;
Δ = b2-4ac
Δ = -202-4·2·(-22)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-24}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+24}{2*2}=\frac{44}{4}
=11
$