15x(2x+2)=10(3x+4)

Solution for 15x(2x+2)=10(3x+4) equation:

15x(2x+2)=10(3x+4)

We move all terms to the left:

15x(2x+2)-(10(3x+4))=0

We multiply parentheses

30x^2+30x-(10(3x+4))=0


We calculate terms in parentheses: -(10(3x+4)), so:

10(3x+4)

We multiply parentheses

30x+40

Back to the equation:

-(30x+40)


We get rid of parentheses

30x^2+30x-30x-40=0

We add all the numbers together, and all the variables

30x^2-40=0

a = 30; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·30·(-40)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*30}=\frac{0-40\sqrt{3}}{60}
=-\frac{40\sqrt{3}}{60}
=-\frac{2\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*30}=\frac{0+40\sqrt{3}}{60}
=\frac{40\sqrt{3}}{60}
=\frac{2\sqrt{3}}{3}
$