x^2+2x+140=25x+50

Solution for x^2+2x+140=25x+50 equation:

x^2+2x+140=25x+50

We move all terms to the left:

x^2+2x+140-(25x+50)=0

We get rid of parentheses

x^2+2x-25x-50+140=0

We add all the numbers together, and all the variables

x^2-23x+90=0

a = 1; b = -23; c = +90;
Δ = b2-4ac
Δ = -232-4·1·90
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*1}=\frac{36}{2}
=18
$