7x^2=11-12x

Solution for 7x^2=11-12x equation:

7x^2=11-12x

We move all terms to the left:

7x^2-(11-12x)=0

We add all the numbers together, and all the variables

7x^2-(-12x+11)=0

We get rid of parentheses

7x^2+12x-11=0

a = 7; b = 12; c = -11;
Δ = b2-4ac
Δ = 122-4·7·(-11)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{113}}{2*7}=\frac{-12-2\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{113}}{2*7}=\frac{-12+2\sqrt{113}}{14}
$