10(2+x)=15x(x-1)+5

Solution for 10(2+x)=15x(x-1)+5 equation:

10(2+x)=15x(x-1)+5

We move all terms to the left:

10(2+x)-(15x(x-1)+5)=0

We add all the numbers together, and all the variables

10(x+2)-(15x(x-1)+5)=0

We multiply parentheses

10x-(15x(x-1)+5)+20=0


We calculate terms in parentheses: -(15x(x-1)+5), so:

15x(x-1)+5

We multiply parentheses

15x^2-15x+5

Back to the equation:

-(15x^2-15x+5)


We get rid of parentheses

-15x^2+10x+15x-5+20=0

We add all the numbers together, and all the variables

-15x^2+25x+15=0

a = -15; b = 25; c = +15;
Δ = b2-4ac
Δ = 252-4·(-15)·15
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{61}}{2*-15}=\frac{-25-5\sqrt{61}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{61}}{2*-15}=\frac{-25+5\sqrt{61}}{-30}
$