5x(3x+8)=2x(7x+6)

Solution for 5x(3x+8)=2x(7x+6) equation:

5x(3x+8)=2x(7x+6)

We move all terms to the left:

5x(3x+8)-(2x(7x+6))=0

We multiply parentheses

15x^2+40x-(2x(7x+6))=0


We calculate terms in parentheses: -(2x(7x+6)), so:

2x(7x+6)

We multiply parentheses

14x^2+12x

Back to the equation:

-(14x^2+12x)


We get rid of parentheses

15x^2-14x^2+40x-12x=0

We add all the numbers together, and all the variables

x^2+28x=0

a = 1; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·1·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*1}=\frac{0}{2}
=0
$