10x^2=19-10x

Solution for 10x^2=19-10x equation:

10x^2=19-10x

We move all terms to the left:

10x^2-(19-10x)=0

We add all the numbers together, and all the variables

10x^2-(-10x+19)=0

We get rid of parentheses

10x^2+10x-19=0

a = 10; b = 10; c = -19;
Δ = b2-4ac
Δ = 102-4·10·(-19)
Δ = 860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{860}=\sqrt{4*215}=\sqrt{4}*\sqrt{215}=2\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{215}}{2*10}=\frac{-10-2\sqrt{215}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{215}}{2*10}=\frac{-10+2\sqrt{215}}{20}
$