x-3-((x-3)*(5/10))+3=4

Solution for x-3-((x-3)*(5/10))+3=4 equation:

x-3-((x-3)(5/10))+3=4

We move all terms to the left:

x-3-((x-3)(5/10))+3-(4)=0

We add all the numbers together, and all the variables

x-((x-3)(+5/10))-3+3-4=0

We add all the numbers together, and all the variables

x-((x-3)(+5/10))-4=0

We multiply parentheses ..

-((+5x^2-3*5/10))+x-4=0

We multiply all the terms by the denominator


-((+5x^2-3*5+x*10))-4*10))=0


We calculate terms in parentheses: -((+5x^2-3*5+x*10)), so:

(+5x^2-3*5+x*10)

We get rid of parentheses

5x^2+x*10-3*5

We add all the numbers together, and all the variables

5x^2+x*10-15

Wy multiply elements

5x^2+10x-15

Back to the equation:

-(5x^2+10x-15)


We add all the numbers together, and all the variables

-(5x^2+10x-15)=0

We get rid of parentheses

-5x^2-10x+15=0

a = -5; b = -10; c = +15;
Δ = b2-4ac
Δ = -102-4·(-5)·15
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-5}=\frac{30}{-10}
=-3
$