374=x^2-5x

Solution for 374=x^2-5x equation:

374=x^2-5x

We move all terms to the left:

374-(x^2-5x)=0

We get rid of parentheses

-x^2+5x+374=0

We add all the numbers together, and all the variables

-1x^2+5x+374=0

a = -1; b = 5; c = +374;
Δ = b2-4ac
Δ = 52-4·(-1)·374
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-39}{2*-1}=\frac{-44}{-2}
=+22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+39}{2*-1}=\frac{34}{-2}
=-17
$