6x+22=25x2

Solution for 6x+22=25x2 equation:

6x+22=25x^2

We move all terms to the left:

6x+22-(25x^2)=0

determiningTheFunctionDomain
-25x^2+6x+22=0

a = -25; b = 6; c = +22;
Δ = b2-4ac
Δ = 62-4·(-25)·22
Δ = 2236
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:

$\sqrt{\Delta}=\sqrt{2236}=\sqrt{4*559}=\sqrt{4}*\sqrt{559}=2\sqrt{559}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{559}}{2*-25}=\frac{-6-2\sqrt{559}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{559}}{2*-25}=\frac{-6+2\sqrt{559}}{-50}
$