2x-11=5(2x+5)6x

Solution for 2x-11=5(2x+5)6x equation:

2x-11=5(2x+5)6x

We move all terms to the left:

2x-11-(5(2x+5)6x)=0


We calculate terms in parentheses: -(5(2x+5)6x), so:

5(2x+5)6x

We multiply parentheses

60x^2+150x

Back to the equation:

-(60x^2+150x)


We get rid of parentheses

-60x^2+2x-150x-11=0

We add all the numbers together, and all the variables

-60x^2-148x-11=0

a = -60; b = -148; c = -11;
Δ = b2-4ac
Δ = -1482-4·(-60)·(-11)
Δ = 19264
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:

$\sqrt{\Delta}=\sqrt{19264}=\sqrt{64*301}=\sqrt{64}*\sqrt{301}=8\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-8\sqrt{301}}{2*-60}=\frac{148-8\sqrt{301}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+8\sqrt{301}}{2*-60}=\frac{148+8\sqrt{301}}{-120}
$