4t-6/2t=5

Solution for 4t-6/2t=5 equation:

4t-6/2t=5

We move all terms to the left:

4t-6/2t-(5)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We multiply all the terms by the denominator


4t*2t-5*2t-6=0

Wy multiply elements

8t^2-10t-6=0

a = 8; b = -10; c = -6;
Δ = b2-4ac
Δ = -102-4·8·(-6)
Δ = 292
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*8}=\frac{10-2\sqrt{73}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*8}=\frac{10+2\sqrt{73}}{16}
$