(5x2-7x-3)=(5x-9)

Solution for (5x2-7x-3)=(5x-9) equation:

(5x^2-7x-3)=(5x-9)

We move all terms to the left:

(5x^2-7x-3)-((5x-9))=0

We get rid of parentheses

5x^2-7x-((5x-9))-3=0


We calculate terms in parentheses: -((5x-9)), so:

(5x-9)

We get rid of parentheses

5x-9

Back to the equation:

-(5x-9)


We get rid of parentheses

5x^2-7x-5x+9-3=0

We add all the numbers together, and all the variables

5x^2-12x+6=0

a = 5; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·5·6
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{6}}{2*5}=\frac{12-2\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*5}=\frac{12+2\sqrt{6}}{10}
$