8x+11=3x(2x+5)

Solution for 8x+11=3x(2x+5) equation:

8x+11=3x(2x+5)

We move all terms to the left:

8x+11-(3x(2x+5))=0


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

3x(2x+5)

We multiply parentheses

6x^2+15x

Back to the equation:

-(6x^2+15x)


We get rid of parentheses

-6x^2+8x-15x+11=0

We add all the numbers together, and all the variables

-6x^2-7x+11=0

a = -6; b = -7; c = +11;
Δ = b2-4ac
Δ = -72-4·(-6)·11
Δ = 313
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{-(-7)-\sqrt{313}}{2*-6}=\frac{7-\sqrt{313}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{313}}{2*-6}=\frac{7+\sqrt{313}}{-12}
$