3x^2=1000+130x

Solution for 3x^2=1000+130x equation:

3x^2=1000+130x

We move all terms to the left:

3x^2-(1000+130x)=0

We add all the numbers together, and all the variables

3x^2-(130x+1000)=0

We get rid of parentheses

3x^2-130x-1000=0

a = 3; b = -130; c = -1000;
Δ = b2-4ac
Δ = -1302-4·3·(-1000)
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-170}{2*3}=\frac{-40}{6}
=-6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+170}{2*3}=\frac{300}{6}
=50
$