4x2+6x+35=16x2+7x

Solution for 4x2+6x+35=16x2+7x equation:

4x^2+6x+35=16x^2+7x

We move all terms to the left:

4x^2+6x+35-(16x^2+7x)=0

We get rid of parentheses

4x^2-16x^2+6x-7x+35=0

We add all the numbers together, and all the variables

-12x^2-1x+35=0

a = -12; b = -1; c = +35;
Δ = b2-4ac
Δ = -12-4·(-12)·35
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*-12}=\frac{42}{-24}
=-1+3/4
$