4-2x(x+7)=3(x+5)

Solution for 4-2x(x+7)=3(x+5) equation:

4-2x(x+7)=3(x+5)

We move all terms to the left:

4-2x(x+7)-(3(x+5))=0

We multiply parentheses

-2x^2-14x-(3(x+5))+4=0


We calculate terms in parentheses: -(3(x+5)), so:

3(x+5)

We multiply parentheses

3x+15

Back to the equation:

-(3x+15)


We get rid of parentheses

-2x^2-14x-3x-15+4=0

We add all the numbers together, and all the variables

-2x^2-17x-11=0

a = -2; b = -17; c = -11;
Δ = b2-4ac
Δ = -172-4·(-2)·(-11)
Δ = 201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{201}}{2*-2}=\frac{17-\sqrt{201}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{201}}{2*-2}=\frac{17+\sqrt{201}}{-4}
$