4(2x+1)=3(x+3)5x

Solution for 4(2x+1)=3(x+3)5x equation:

4(2x+1)=3(x+3)5x

We move all terms to the left:

4(2x+1)-(3(x+3)5x)=0

We multiply parentheses

8x-(3(x+3)5x)+4=0


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

3(x+3)5x

We multiply parentheses

15x^2+45x

Back to the equation:

-(15x^2+45x)


We get rid of parentheses

-15x^2+8x-45x+4=0

We add all the numbers together, and all the variables

-15x^2-37x+4=0

a = -15; b = -37; c = +4;
Δ = b2-4ac
Δ = -372-4·(-15)·4
Δ = 1609
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{-(-37)-\sqrt{1609}}{2*-15}=\frac{37-\sqrt{1609}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1609}}{2*-15}=\frac{37+\sqrt{1609}}{-30}
$