5x(2x+3)=3(x+8)

Solution for 5x(2x+3)=3(x+8) equation:

5x(2x+3)=3(x+8)

We move all terms to the left:

5x(2x+3)-(3(x+8))=0

We multiply parentheses

10x^2+15x-(3(x+8))=0


We calculate terms in parentheses: -(3(x+8)), so:

3(x+8)

We multiply parentheses

3x+24

Back to the equation:

-(3x+24)


We get rid of parentheses

10x^2+15x-3x-24=0

We add all the numbers together, and all the variables

10x^2+12x-24=0

a = 10; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·10·(-24)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{69}}{2*10}=\frac{-12-4\sqrt{69}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{69}}{2*10}=\frac{-12+4\sqrt{69}}{20}
$