(x+4)(2x-1)=1-(3x-7)

Solution for (x+4)(2x-1)=1-(3x-7) equation:

(x+4)(2x-1)=1-(3x-7)

We move all terms to the left:

(x+4)(2x-1)-(1-(3x-7))=0

We multiply parentheses ..

(+2x^2-1x+8x-4)-(1-(3x-7))=0


We calculate terms in parentheses: -(1-(3x-7)), so:

1-(3x-7)

determiningTheFunctionDomain
-(3x-7)+1

We get rid of parentheses

-3x+7+1

We add all the numbers together, and all the variables

-3x+8

Back to the equation:

-(-3x+8)


We get rid of parentheses

2x^2-1x+8x+3x-4-8=0

We add all the numbers together, and all the variables

2x^2+10x-12=0

a = 2; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·2·(-12)
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{-(10)-14}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*2}=\frac{4}{4}
=1
$