-22(x)+8(x)^2=133

Solution for -22(x)+8(x)^2=133 equation:

-22(x)+8(x)^2=133

We move all terms to the left:

-22(x)+8(x)^2-(133)=0

determiningTheFunctionDomain
8x^2-22x-133=0

a = 8; b = -22; c = -133;
Δ = b2-4ac
Δ = -222-4·8·(-133)
Δ = 4740
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:

$\sqrt{\Delta}=\sqrt{4740}=\sqrt{4*1185}=\sqrt{4}*\sqrt{1185}=2\sqrt{1185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{1185}}{2*8}=\frac{22-2\sqrt{1185}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{1185}}{2*8}=\frac{22+2\sqrt{1185}}{16}
$