10x+25=5x^2+30x

Solution for 10x+25=5x^2+30x equation:

10x+25=5x^2+30x

We move all terms to the left:

10x+25-(5x^2+30x)=0

We get rid of parentheses

-5x^2+10x-30x+25=0

We add all the numbers together, and all the variables

-5x^2-20x+25=0

a = -5; b = -20; c = +25;
Δ = b2-4ac
Δ = -202-4·(-5)·25
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-30}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+30}{2*-5}=\frac{50}{-10}
=-5
$