8(4-x)=7x2

Solution for 8(4-x)=7x2 equation:

8(4-x)=7x^2

We move all terms to the left:

8(4-x)-(7x^2)=0

determiningTheFunctionDomain
-7x^2+8(4-x)=0

We add all the numbers together, and all the variables

-7x^2+8(-1x+4)=0

We multiply parentheses

-7x^2-8x+32=0

a = -7; b = -8; c = +32;
Δ = b2-4ac
Δ = -82-4·(-7)·32
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{15}}{2*-7}=\frac{8-8\sqrt{15}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{15}}{2*-7}=\frac{8+8\sqrt{15}}{-14}
$