(7x+2)=(8x2-8)

Solution for (7x+2)=(8x2-8) equation:

(7x+2)=(8x^2-8)

We move all terms to the left:

(7x+2)-((8x^2-8))=0

We get rid of parentheses

7x-((8x^2-8))+2=0


We calculate terms in parentheses: -((8x^2-8)), so:

(8x^2-8)

We get rid of parentheses

8x^2-8

Back to the equation:

-(8x^2-8)


We get rid of parentheses

-8x^2+7x+8+2=0

We add all the numbers together, and all the variables

-8x^2+7x+10=0

a = -8; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·(-8)·10
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{41}}{2*-8}=\frac{-7-3\sqrt{41}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{41}}{2*-8}=\frac{-7+3\sqrt{41}}{-16}
$