4+3/4a=7/8a-10

Solution for 4+3/4a=7/8a-10 equation:

4+3/4a=7/8a-10

We move all terms to the left:

4+3/4a-(7/8a-10)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a-10)!=0

a∈R


We get rid of parentheses

3/4a-7/8a+10+4=0

We calculate fractions


24a/32a^2+(-28a)/32a^2+10+4=0

We add all the numbers together, and all the variables

24a/32a^2+(-28a)/32a^2+14=0

We multiply all the terms by the denominator


24a+(-28a)+14*32a^2=0

Wy multiply elements

448a^2+24a+(-28a)=0

We get rid of parentheses

448a^2+24a-28a=0

We add all the numbers together, and all the variables

448a^2-4a=0

a = 448; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·448·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*448}=\frac{0}{896}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*448}=\frac{8}{896}
=1/112
$