Y=7x+1/4x-5

Solution for Y=7x+1/4x-5 equation:

=7Y+1/4Y-5

We move all terms to the left:

-(7Y+1/4Y-5)=0


Domain of the equation: 4Y-5)!=0

Y∈R


We get rid of parentheses

-7Y-1/4Y+5=0

We multiply all the terms by the denominator


-7Y*4Y+5*4Y-1=0

Wy multiply elements

-28Y^2+20Y-1=0

a = -28; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-28)·(-1)
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{2}}{2*-28}=\frac{-20-12\sqrt{2}}{-56}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{2}}{2*-28}=\frac{-20+12\sqrt{2}}{-56}
$