11x2=7+5x

Solution for 11x2=7+5x equation:

11x^2=7+5x

We move all terms to the left:

11x^2-(7+5x)=0

We add all the numbers together, and all the variables

11x^2-(5x+7)=0

We get rid of parentheses

11x^2-5x-7=0

a = 11; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·11·(-7)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{37}}{2*11}=\frac{5-3\sqrt{37}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{37}}{2*11}=\frac{5+3\sqrt{37}}{22}
$