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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(3x+5)

We multiply parentheses

6x+10

Back to the equation:

-(6x+10)


We get rid of parentheses

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

We add all the numbers together, and all the variables

28x^2+8x-10=0

a = 28; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·28·(-10)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{74}}{2*28}=\frac{-8-4\sqrt{74}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{74}}{2*28}=\frac{-8+4\sqrt{74}}{56}
$