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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2-8x-(7(3x+2))=0


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

7(3x+2)

We multiply parentheses

21x+14

Back to the equation:

-(21x+14)


We get rid of parentheses

2x^2-8x-21x-14=0

We add all the numbers together, and all the variables

2x^2-29x-14=0

a = 2; b = -29; c = -14;
Δ = b2-4ac
Δ = -292-4·2·(-14)
Δ = 953
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{-(-29)-\sqrt{953}}{2*2}=\frac{29-\sqrt{953}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{953}}{2*2}=\frac{29+\sqrt{953}}{4}
$