110*7/22=x*x

Solution for 110*7/22=x*x equation:

110*7/22=x*x

We move all terms to the left:

110*7/22-(x*x)=0

We add all the numbers together, and all the variables

-(+x*x)+110*7/22=0

We get rid of parentheses

-x*x+110*7/22=0

We multiply all the terms by the denominator


-(x*x)*22+110*7=0

We add all the numbers together, and all the variables

-(+x*x)*22+110*7=0

We add all the numbers together, and all the variables

-(+x*x)*22+770=0

We multiply parentheses

-22x^2+770=0

a = -22; b = 0; c = +770;
Δ = b2-4ac
Δ = 02-4·(-22)·770
Δ = 67760
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:

$\sqrt{\Delta}=\sqrt{67760}=\sqrt{1936*35}=\sqrt{1936}*\sqrt{35}=44\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44\sqrt{35}}{2*-22}=\frac{0-44\sqrt{35}}{-44}
=-\frac{44\sqrt{35}}{-44}
=-\frac{\sqrt{35}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44\sqrt{35}}{2*-22}=\frac{0+44\sqrt{35}}{-44}
=\frac{44\sqrt{35}}{-44}
=\frac{\sqrt{35}}{-1}
$