75=2x(3+x)

Solution for 75=2x(3+x) equation:

75=2x(3+x)

We move all terms to the left:

75-(2x(3+x))=0

We add all the numbers together, and all the variables

-(2x(x+3))+75=0


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

2x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

-2x^2-6x+75=0

a = -2; b = -6; c = +75;
Δ = b2-4ac
Δ = -62-4·(-2)·75
Δ = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{159}}{2*-2}=\frac{6-2\sqrt{159}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{159}}{2*-2}=\frac{6+2\sqrt{159}}{-4}
$