10x+2=25x^2+5x

Solution for 10x+2=25x^2+5x equation:

10x+2=25x^2+5x

We move all terms to the left:

10x+2-(25x^2+5x)=0

We get rid of parentheses

-25x^2+10x-5x+2=0

We add all the numbers together, and all the variables

-25x^2+5x+2=0

a = -25; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-25)·2
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*-25}=\frac{-20}{-50}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*-25}=\frac{10}{-50}
=-1/5
$