5x^2=22+10x

Solution for 5x^2=22+10x equation:

5x^2=22+10x

We move all terms to the left:

5x^2-(22+10x)=0

We add all the numbers together, and all the variables

5x^2-(10x+22)=0

We get rid of parentheses

5x^2-10x-22=0

a = 5; b = -10; c = -22;
Δ = b2-4ac
Δ = -102-4·5·(-22)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{15}}{2*5}=\frac{10-6\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{15}}{2*5}=\frac{10+6\sqrt{15}}{10}
$