7=2(x+9)8x

Solution for 7=2(x+9)8x equation:

7=2(x+9)8x

We move all terms to the left:

7-(2(x+9)8x)=0


We calculate terms in parentheses: -(2(x+9)8x), so:

2(x+9)8x

We multiply parentheses

16x^2+144x

Back to the equation:

-(16x^2+144x)


We get rid of parentheses

-16x^2-144x+7=0

a = -16; b = -144; c = +7;
Δ = b2-4ac
Δ = -1442-4·(-16)·7
Δ = 21184
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:

$\sqrt{\Delta}=\sqrt{21184}=\sqrt{64*331}=\sqrt{64}*\sqrt{331}=8\sqrt{331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{331}}{2*-16}=\frac{144-8\sqrt{331}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{331}}{2*-16}=\frac{144+8\sqrt{331}}{-32}
$