x^2+x=45/60

Solution for x^2+x=45/60 equation:

x^2+x=45/60

We move all terms to the left:

x^2+x-(45/60)=0

We add all the numbers together, and all the variables

x^2+x-(+45/60)=0

We get rid of parentheses

x^2+x-45/60=0

We multiply all the terms by the denominator


x^2*60+x*60-45=0

Wy multiply elements

60x^2+60x-45=0

a = 60; b = 60; c = -45;
Δ = b2-4ac
Δ = 602-4·60·(-45)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-120}{2*60}=\frac{-180}{120}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+120}{2*60}=\frac{60}{120}
=1/2
$