172=4(6x-11)x=

Solution for 172=4(6x-11)x= equation:

172=4(6x-11)x=

We move all terms to the left:

172-(4(6x-11)x)=0


We calculate terms in parentheses: -(4(6x-11)x), so:

4(6x-11)x

We multiply parentheses

24x^2-44x

Back to the equation:

-(24x^2-44x)


We get rid of parentheses

-24x^2+44x+172=0

a = -24; b = 44; c = +172;
Δ = b2-4ac
Δ = 442-4·(-24)·172
Δ = 18448
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:

$\sqrt{\Delta}=\sqrt{18448}=\sqrt{16*1153}=\sqrt{16}*\sqrt{1153}=4\sqrt{1153}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{1153}}{2*-24}=\frac{-44-4\sqrt{1153}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{1153}}{2*-24}=\frac{-44+4\sqrt{1153}}{-48}
$