0=3x^2+8x-175

Solution for 0=3x^2+8x-175 equation:

0=3x^2+8x-175

We move all terms to the left:

0-(3x^2+8x-175)=0

We add all the numbers together, and all the variables

-(3x^2+8x-175)=0

We get rid of parentheses

-3x^2-8x+175=0

a = -3; b = -8; c = +175;
Δ = b2-4ac
Δ = -82-4·(-3)·175
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{541}}{2*-3}=\frac{8-2\sqrt{541}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{541}}{2*-3}=\frac{8+2\sqrt{541}}{-6}
$