-5x(22x-7)=4-3x(x+5)

Solution for -5x(22x-7)=4-3x(x+5) equation:

-5x(22x-7)=4-3x(x+5)

We move all terms to the left:

-5x(22x-7)-(4-3x(x+5))=0

We multiply parentheses

-110x^2+35x-(4-3x(x+5))=0


We calculate terms in parentheses: -(4-3x(x+5)), so:

4-3x(x+5)

determiningTheFunctionDomain
-3x(x+5)+4

We multiply parentheses

-3x^2-15x+4

Back to the equation:

-(-3x^2-15x+4)


We get rid of parentheses

-110x^2+3x^2+15x+35x-4=0

We add all the numbers together, and all the variables

-107x^2+50x-4=0

a = -107; b = 50; c = -4;
Δ = b2-4ac
Δ = 502-4·(-107)·(-4)
Δ = 788
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:

$\sqrt{\Delta}=\sqrt{788}=\sqrt{4*197}=\sqrt{4}*\sqrt{197}=2\sqrt{197}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{197}}{2*-107}=\frac{-50-2\sqrt{197}}{-214}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{197}}{2*-107}=\frac{-50+2\sqrt{197}}{-214}
$