10x^2=50x-40x^2

Solution for 10x^2=50x-40x^2 equation:

10x^2=50x-40x^2

We move all terms to the left:

10x^2-(50x-40x^2)=0

We get rid of parentheses

10x^2+40x^2-50x=0

We add all the numbers together, and all the variables

50x^2-50x=0

a = 50; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·50·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*50}=\frac{100}{100}
=1
$