Y=x2-5x-3Y=2x+5

Solution for Y=x2-5x-3Y=2x+5 equation:

=Y2-5Y-3=2Y+5

We move all terms to the left:

-(Y2-5Y-3)=0

We add all the numbers together, and all the variables

-(+Y^2-5Y-3)=0

We get rid of parentheses

-Y^2+5Y+3=0

We add all the numbers together, and all the variables

-1Y^2+5Y+3=0

a = -1; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-1)·3
Δ = 37
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{37}}{2*-1}=\frac{-5-\sqrt{37}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*-1}=\frac{-5+\sqrt{37}}{-2}
$