5(x2)=6(x+4)

Solution for 5(x2)=6(x+4) equation:

5(x2)=6(x+4)

We move all terms to the left:

5(x2)-(6(x+4))=0

We add all the numbers together, and all the variables

5x^2-(6(x+4))=0


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

6(x+4)

We multiply parentheses

6x+24

Back to the equation:

-(6x+24)


We get rid of parentheses

5x^2-6x-24=0

a = 5; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·5·(-24)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{129}}{2*5}=\frac{6-2\sqrt{129}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{129}}{2*5}=\frac{6+2\sqrt{129}}{10}
$