12x=7x^2-64

Solution for 12x=7x^2-64 equation:

12x=7x^2-64

We move all terms to the left:

12x-(7x^2-64)=0

We get rid of parentheses

-7x^2+12x+64=0

a = -7; b = 12; c = +64;
Δ = b2-4ac
Δ = 122-4·(-7)·64
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-44}{2*-7}=\frac{-56}{-14}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+44}{2*-7}=\frac{32}{-14}
=-2+2/7
$