15x+3x(x-1)=8(x+2)-10

Solution for 15x+3x(x-1)=8(x+2)-10 equation:

15x+3x(x-1)=8(x+2)-10

We move all terms to the left:

15x+3x(x-1)-(8(x+2)-10)=0

We multiply parentheses

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


We calculate terms in parentheses: -(8(x+2)-10), so:

8(x+2)-10

We multiply parentheses

8x+16-10

We add all the numbers together, and all the variables

8x+6

Back to the equation:

-(8x+6)


We add all the numbers together, and all the variables

3x^2+12x-(8x+6)=0

We get rid of parentheses

3x^2+12x-8x-6=0

We add all the numbers together, and all the variables

3x^2+4x-6=0

a = 3; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·3·(-6)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{22}}{2*3}=\frac{-4-2\sqrt{22}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{22}}{2*3}=\frac{-4+2\sqrt{22}}{6}
$