4x2=35+13x

Solution for 4x2=35+13x equation:

4x^2=35+13x

We move all terms to the left:

4x^2-(35+13x)=0

We add all the numbers together, and all the variables

4x^2-(13x+35)=0

We get rid of parentheses

4x^2-13x-35=0

a = 4; b = -13; c = -35;
Δ = b2-4ac
Δ = -132-4·4·(-35)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-27}{2*4}=\frac{-14}{8}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+27}{2*4}=\frac{40}{8}
=5
$