12x-7+5x=8(2x+1)x-8

Solution for 12x-7+5x=8(2x+1)x-8 equation:

12x-7+5x=8(2x+1)x-8

We move all terms to the left:

12x-7+5x-(8(2x+1)x-8)=0

We add all the numbers together, and all the variables

17x-(8(2x+1)x-8)-7=0


We calculate terms in parentheses: -(8(2x+1)x-8), so:

8(2x+1)x-8

We multiply parentheses

16x^2+8x-8

Back to the equation:

-(16x^2+8x-8)


We get rid of parentheses

-16x^2+17x-8x+8-7=0

We add all the numbers together, and all the variables

-16x^2+9x+1=0

a = -16; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·(-16)·1
Δ = 145
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{-(9)-\sqrt{145}}{2*-16}=\frac{-9-\sqrt{145}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{145}}{2*-16}=\frac{-9+\sqrt{145}}{-32}
$