0=10x^2-45x-21

Solution for 0=10x^2-45x-21 equation:

0=10x^2-45x-21

We move all terms to the left:

0-(10x^2-45x-21)=0

We add all the numbers together, and all the variables

-(10x^2-45x-21)=0

We get rid of parentheses

-10x^2+45x+21=0

a = -10; b = 45; c = +21;
Δ = b2-4ac
Δ = 452-4·(-10)·21
Δ = 2865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2865}}{2*-10}=\frac{-45-\sqrt{2865}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2865}}{2*-10}=\frac{-45+\sqrt{2865}}{-20}
$