-9/4x+7+1/2x+4=10

Solution for -9/4x+7+1/2x+4=10 equation:

-9/4x+7+1/2x+4=10

We move all terms to the left:

-9/4x+7+1/2x+4-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-9/4x+1/2x+1=0

We calculate fractions


(-18x)/8x^2+4x/8x^2+1=0

We multiply all the terms by the denominator


(-18x)+4x+1*8x^2=0

We add all the numbers together, and all the variables

4x+(-18x)+1*8x^2=0

Wy multiply elements

8x^2+4x+(-18x)=0

We get rid of parentheses

8x^2+4x-18x=0

We add all the numbers together, and all the variables

8x^2-14x=0

a = 8; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·8·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*8}=\frac{28}{16}
=1+3/4
$