7x+12+3x=-6(x-7)*8x

Solution for 7x+12+3x=-6(x-7)*8x equation:

7x+12+3x=-6(x-7)*8x

We move all terms to the left:

7x+12+3x-(-6(x-7)*8x)=0

We add all the numbers together, and all the variables

10x-(-6(x-7)*8x)+12=0


We calculate terms in parentheses: -(-6(x-7)*8x), so:

-6(x-7)*8x

We multiply parentheses

-48x^2+336x

Back to the equation:

-(-48x^2+336x)


We get rid of parentheses

48x^2-336x+10x+12=0

We add all the numbers together, and all the variables

48x^2-326x+12=0

a = 48; b = -326; c = +12;
Δ = b2-4ac
Δ = -3262-4·48·12
Δ = 103972
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:

$\sqrt{\Delta}=\sqrt{103972}=\sqrt{4*25993}=\sqrt{4}*\sqrt{25993}=2\sqrt{25993}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-326)-2\sqrt{25993}}{2*48}=\frac{326-2\sqrt{25993}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-326)+2\sqrt{25993}}{2*48}=\frac{326+2\sqrt{25993}}{96}
$