(X+7)-5=4(x+3)6x

Solution for (X+7)-5=4(x+3)6x equation:

(X+7)-5=4(X+3)6X

We move all terms to the left:

(X+7)-5-(4(X+3)6X)=0

We get rid of parentheses

X-(4(X+3)6X)+7-5=0


We calculate terms in parentheses: -(4(X+3)6X), so:

4(X+3)6X

We multiply parentheses

24X^2+72X

Back to the equation:

-(24X^2+72X)


We add all the numbers together, and all the variables

X-(24X^2+72X)+2=0

We get rid of parentheses

-24X^2+X-72X+2=0

We add all the numbers together, and all the variables

-24X^2-71X+2=0

a = -24; b = -71; c = +2;
Δ = b2-4ac
Δ = -712-4·(-24)·2
Δ = 5233
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{-(-71)-\sqrt{5233}}{2*-24}=\frac{71-\sqrt{5233}}{-48}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+\sqrt{5233}}{2*-24}=\frac{71+\sqrt{5233}}{-48}
$