30x+30x^2=100-70x

Solution for 30x+30x^2=100-70x equation:

30x+30x^2=100-70x

We move all terms to the left:

30x+30x^2-(100-70x)=0

We add all the numbers together, and all the variables

30x^2+30x-(-70x+100)=0

We get rid of parentheses

30x^2+30x+70x-100=0

We add all the numbers together, and all the variables

30x^2+100x-100=0

a = 30; b = 100; c = -100;
Δ = b2-4ac
Δ = 1002-4·30·(-100)
Δ = 22000
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:

$\sqrt{\Delta}=\sqrt{22000}=\sqrt{400*55}=\sqrt{400}*\sqrt{55}=20\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{55}}{2*30}=\frac{-100-20\sqrt{55}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{55}}{2*30}=\frac{-100+20\sqrt{55}}{60}
$