x^2-17x-74=10+2x

Solution for x^2-17x-74=10+2x equation:

x^2-17x-74=10+2x

We move all terms to the left:

x^2-17x-74-(10+2x)=0

We add all the numbers together, and all the variables

x^2-17x-(2x+10)-74=0

We get rid of parentheses

x^2-17x-2x-10-74=0

We add all the numbers together, and all the variables

x^2-19x-84=0

a = 1; b = -19; c = -84;
Δ = b2-4ac
Δ = -192-4·1·(-84)
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{697}}{2*1}=\frac{19-\sqrt{697}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{697}}{2*1}=\frac{19+\sqrt{697}}{2}
$