11x^2=-14x+16

Solution for 11x^2=-14x+16 equation:

11x^2=-14x+16

We move all terms to the left:

11x^2-(-14x+16)=0

We get rid of parentheses

11x^2+14x-16=0

a = 11; b = 14; c = -16;
Δ = b2-4ac
Δ = 142-4·11·(-16)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-30}{2*11}=\frac{-44}{22}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+30}{2*11}=\frac{16}{22}
=8/11
$