0=10x^2-20x-35

Solution for 0=10x^2-20x-35 equation:

0=10x^2-20x-35

We move all terms to the left:

0-(10x^2-20x-35)=0

We add all the numbers together, and all the variables

-(10x^2-20x-35)=0

We get rid of parentheses

-10x^2+20x+35=0

a = -10; b = 20; c = +35;
Δ = b2-4ac
Δ = 202-4·(-10)·35
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-30\sqrt{2}}{2*-10}=\frac{-20-30\sqrt{2}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+30\sqrt{2}}{2*-10}=\frac{-20+30\sqrt{2}}{-20}
$