Y=7x^2+2x^2+5x-6

Solution for Y=7x^2+2x^2+5x-6 equation:

=7Y^2+2Y^2+5Y-6

We move all terms to the left:

-(7Y^2+2Y^2+5Y-6)=0

We get rid of parentheses

-7Y^2-2Y^2-5Y+6=0

We add all the numbers together, and all the variables

-9Y^2-5Y+6=0

a = -9; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-9)·6
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{241}}{2*-9}=\frac{5-\sqrt{241}}{-18}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*-9}=\frac{5+\sqrt{241}}{-18}
$