2(10x+8)-1=5x(x-6)

Solution for 2(10x+8)-1=5x(x-6) equation:

2(10x+8)-1=5x(x-6)

We move all terms to the left:

2(10x+8)-1-(5x(x-6))=0

We multiply parentheses

20x-(5x(x-6))+16-1=0


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

5x(x-6)

We multiply parentheses

5x^2-30x

Back to the equation:

-(5x^2-30x)


We add all the numbers together, and all the variables

20x-(5x^2-30x)+15=0

We get rid of parentheses

-5x^2+20x+30x+15=0

We add all the numbers together, and all the variables

-5x^2+50x+15=0

a = -5; b = 50; c = +15;
Δ = b2-4ac
Δ = 502-4·(-5)·15
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-20\sqrt{7}}{2*-5}=\frac{-50-20\sqrt{7}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+20\sqrt{7}}{2*-5}=\frac{-50+20\sqrt{7}}{-10}
$