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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-10x^2-5x+3=0

a = -10; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-10)·3
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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