Y=10x^2-140x-320

Solution for Y=10x^2-140x-320 equation:

=10Y^2-140Y-320

We move all terms to the left:

-(10Y^2-140Y-320)=0

We get rid of parentheses

-10Y^2+140Y+320=0

a = -10; b = 140; c = +320;
Δ = b2-4ac
Δ = 1402-4·(-10)·320
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-180}{2*-10}=\frac{-320}{-20}
=+16
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+180}{2*-10}=\frac{40}{-20}
=-2
$