4x^2+5=8x+7

Solution for 4x^2+5=8x+7 equation:

4x^2+5=8x+7

We move all terms to the left:

4x^2+5-(8x+7)=0

We get rid of parentheses

4x^2-8x-7+5=0

We add all the numbers together, and all the variables

4x^2-8x-2=0

a = 4; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·4·(-2)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*4}=\frac{8-4\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*4}=\frac{8+4\sqrt{6}}{8}
$