-4x(x-11)-34=10-12

Solution for -4x(x-11)-34=10-12 equation:

-4x(x-11)-34=10-12

We move all terms to the left:

-4x(x-11)-34-(10-12)=0

We add all the numbers together, and all the variables

-4x(x-11)-34-(-2)=0

We add all the numbers together, and all the variables

-4x(x-11)-32=0

We multiply parentheses

-4x^2+44x-32=0

a = -4; b = 44; c = -32;
Δ = b2-4ac
Δ = 442-4·(-4)·(-32)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{89}}{2*-4}=\frac{-44-4\sqrt{89}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{89}}{2*-4}=\frac{-44+4\sqrt{89}}{-8}
$