22x2=10x+74

Solution for 22x2=10x+74 equation:

22x^2=10x+74

We move all terms to the left:

22x^2-(10x+74)=0

We get rid of parentheses

22x^2-10x-74=0

a = 22; b = -10; c = -74;
Δ = b2-4ac
Δ = -102-4·22·(-74)
Δ = 6612
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:

$\sqrt{\Delta}=\sqrt{6612}=\sqrt{4*1653}=\sqrt{4}*\sqrt{1653}=2\sqrt{1653}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1653}}{2*22}=\frac{10-2\sqrt{1653}}{44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1653}}{2*22}=\frac{10+2\sqrt{1653}}{44}
$