(5x^2+9-4)=(5x+6)

Solution for (5x^2+9-4)=(5x+6) equation:

(5x^2+9-4)=(5x+6)

We move all terms to the left:

(5x^2+9-4)-((5x+6))=0

We get rid of parentheses

5x^2-((5x+6))+9-4=0


We calculate terms in parentheses: -((5x+6)), so:

(5x+6)

We get rid of parentheses

5x+6

Back to the equation:

-(5x+6)


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x^2-5x-6+5=0

We add all the numbers together, and all the variables

5x^2-5x-1=0

a = 5; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·5·(-1)
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*5}=\frac{5-3\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*5}=\frac{5+3\sqrt{5}}{10}
$