61/4a-10=6a-15

Solution for 61/4a-10=6a-15 equation:

61/4a-10=6a-15

We move all terms to the left:

61/4a-10-(6a-15)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We get rid of parentheses

61/4a-6a+15-10=0

We multiply all the terms by the denominator


-6a*4a+15*4a-10*4a+61=0

Wy multiply elements

-24a^2+60a-40a+61=0

We add all the numbers together, and all the variables

-24a^2+20a+61=0

a = -24; b = 20; c = +61;
Δ = b2-4ac
Δ = 202-4·(-24)·61
Δ = 6256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6256}=\sqrt{16*391}=\sqrt{16}*\sqrt{391}=4\sqrt{391}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{391}}{2*-24}=\frac{-20-4\sqrt{391}}{-48}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{391}}{2*-24}=\frac{-20+4\sqrt{391}}{-48}
$