Y=10x2-7x-12

Solution for Y=10x2-7x-12 equation:

=10Y^2-7Y-12

We move all terms to the left:

-(10Y^2-7Y-12)=0

We get rid of parentheses

-10Y^2+7Y+12=0

a = -10; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-10)·12
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*-10}=\frac{-30}{-20}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*-10}=\frac{16}{-20}
=-4/5
$