4x+7=6x^2-8+5

Solution for 4x+7=6x^2-8+5 equation:

4x+7=6x^2-8+5

We move all terms to the left:

4x+7-(6x^2-8+5)=0

We get rid of parentheses

-6x^2+4x+8-5+7=0

We add all the numbers together, and all the variables

-6x^2+4x+10=0

a = -6; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-6)·10
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*-6}=\frac{12}{-12}
=-1
$