(3x-10)(x+50)=960

Solution for (3x-10)(x+50)=960 equation:

(3x-10)(x+50)=960

We move all terms to the left:

(3x-10)(x+50)-(960)=0

We multiply parentheses ..

(+3x^2+150x-10x-500)-960=0

We get rid of parentheses

3x^2+150x-10x-500-960=0

We add all the numbers together, and all the variables

3x^2+140x-1460=0

a = 3; b = 140; c = -1460;
Δ = b2-4ac
Δ = 1402-4·3·(-1460)
Δ = 37120
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:

$\sqrt{\Delta}=\sqrt{37120}=\sqrt{256*145}=\sqrt{256}*\sqrt{145}=16\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-16\sqrt{145}}{2*3}=\frac{-140-16\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+16\sqrt{145}}{2*3}=\frac{-140+16\sqrt{145}}{6}
$