10x2=5x+50

Solution for 10x2=5x+50 equation:

10x^2=5x+50

We move all terms to the left:

10x^2-(5x+50)=0

We get rid of parentheses

10x^2-5x-50=0

a = 10; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·10·(-50)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*10}=\frac{-40}{20}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*10}=\frac{50}{20}
=2+1/2
$