(6x-9)=(4x^2-7)

Solution for (6x-9)=(4x^2-7) equation:

(6x-9)=(4x^2-7)

We move all terms to the left:

(6x-9)-((4x^2-7))=0

We get rid of parentheses

6x-((4x^2-7))-9=0


We calculate terms in parentheses: -((4x^2-7)), so:

(4x^2-7)

We get rid of parentheses

4x^2-7

Back to the equation:

-(4x^2-7)


We get rid of parentheses

-4x^2+6x+7-9=0

We add all the numbers together, and all the variables

-4x^2+6x-2=0

a = -4; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·(-4)·(-2)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*-4}=\frac{-4}{-8}
=1/2
$