4/5x+7=2x-11

Solution for 4/5x+7=2x-11 equation:

4/5x+7=2x-11

We move all terms to the left:

4/5x+7-(2x-11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

4/5x-2x+11+7=0

We multiply all the terms by the denominator


-2x*5x+11*5x+7*5x+4=0

Wy multiply elements

-10x^2+55x+35x+4=0

We add all the numbers together, and all the variables

-10x^2+90x+4=0

a = -10; b = 90; c = +4;
Δ = b2-4ac
Δ = 902-4·(-10)·4
Δ = 8260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8260}=\sqrt{4*2065}=\sqrt{4}*\sqrt{2065}=2\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2065}}{2*-10}=\frac{-90-2\sqrt{2065}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2065}}{2*-10}=\frac{-90+2\sqrt{2065}}{-20}
$