8+(7-4x^2)=1

Solution for 8+(7-4x^2)=1 equation:

8+(7-4x^2)=1

We move all terms to the left:

8+(7-4x^2)-(1)=0

We add all the numbers together, and all the variables

(7-4x^2)+7=0

We get rid of parentheses

-4x^2+7+7=0

We add all the numbers together, and all the variables

-4x^2+14=0

a = -4; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-4)·14
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*-4}=\frac{0-4\sqrt{14}}{-8}
=-\frac{4\sqrt{14}}{-8}
=-\frac{\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*-4}=\frac{0+4\sqrt{14}}{-8}
=\frac{4\sqrt{14}}{-8}
=\frac{\sqrt{14}}{-2}
$