11x2=7-2x

Solution for 11x2=7-2x equation:

11x^2=7-2x

We move all terms to the left:

11x^2-(7-2x)=0

We add all the numbers together, and all the variables

11x^2-(-2x+7)=0

We get rid of parentheses

11x^2+2x-7=0

a = 11; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·11·(-7)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{78}}{2*11}=\frac{-2-2\sqrt{78}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{78}}{2*11}=\frac{-2+2\sqrt{78}}{22}
$