(x*x)+x=75

Solution for (x*x)+x=75 equation:

(x*x)+x=75

We move all terms to the left:

(x*x)+x-(75)=0

We add all the numbers together, and all the variables

(+x*x)+x-75=0

We add all the numbers together, and all the variables

x+(+x*x)-75=0

We get rid of parentheses

x+x*x-75=0

Wy multiply elements

x^2+x-75=0

a = 1; b = 1; c = -75;
Δ = b2-4ac
Δ = 12-4·1·(-75)
Δ = 301
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{-(1)-\sqrt{301}}{2*1}=\frac{-1-\sqrt{301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{301}}{2*1}=\frac{-1+\sqrt{301}}{2}
$