(x+32)=2x(5x+3)

Solution for (x+32)=2x(5x+3) equation:

(x+32)=2x(5x+3)

We move all terms to the left:

(x+32)-(2x(5x+3))=0

We get rid of parentheses

x-(2x(5x+3))+32=0


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

2x(5x+3)

We multiply parentheses

10x^2+6x

Back to the equation:

-(10x^2+6x)


We get rid of parentheses

-10x^2+x-6x+32=0

We add all the numbers together, and all the variables

-10x^2-5x+32=0

a = -10; b = -5; c = +32;
Δ = b2-4ac
Δ = -52-4·(-10)·32
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{145}}{2*-10}=\frac{5-3\sqrt{145}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{145}}{2*-10}=\frac{5+3\sqrt{145}}{-20}
$