x^2=10x+74

Solution for x^2=10x+74 equation:

x^2=10x+74

We move all terms to the left:

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

We get rid of parentheses

x^2-10x-74=0

a = 1; b = -10; c = -74;
Δ = b2-4ac
Δ = -102-4·1·(-74)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{11}}{2*1}=\frac{10-6\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{11}}{2*1}=\frac{10+6\sqrt{11}}{2}
$