-x+90=-3/5x+74

Solution for -x+90=-3/5x+74 equation:

-x+90=-3/5x+74

We move all terms to the left:

-x+90-(-3/5x+74)=0


Domain of the equation: 5x+74)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(-3/5x+74)+90=0

We get rid of parentheses

-1x+3/5x-74+90=0

We multiply all the terms by the denominator


-1x*5x-74*5x+90*5x+3=0

Wy multiply elements

-5x^2-370x+450x+3=0

We add all the numbers together, and all the variables

-5x^2+80x+3=0

a = -5; b = 80; c = +3;
Δ = b2-4ac
Δ = 802-4·(-5)·3
Δ = 6460
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:

$\sqrt{\Delta}=\sqrt{6460}=\sqrt{4*1615}=\sqrt{4}*\sqrt{1615}=2\sqrt{1615}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1615}}{2*-5}=\frac{-80-2\sqrt{1615}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1615}}{2*-5}=\frac{-80+2\sqrt{1615}}{-10}
$