1/8x+7=-3/4x+78

Solution for 1/8x+7=-3/4x+78 equation:

1/8x+7=-3/4x+78

We move all terms to the left:

1/8x+7-(-3/4x+78)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+78)!=0

x∈R


We get rid of parentheses

1/8x+3/4x-78+7=0

We calculate fractions


4x/32x^2+24x/32x^2-78+7=0

We add all the numbers together, and all the variables

4x/32x^2+24x/32x^2-71=0

We multiply all the terms by the denominator


4x+24x-71*32x^2=0

We add all the numbers together, and all the variables

28x-71*32x^2=0

Wy multiply elements

-2272x^2+28x=0

a = -2272; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-2272)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-2272}=\frac{-56}{-4544}
=7/568
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-2272}=\frac{0}{-4544}
=0
$