13(x)=4x^2-3x+7

Solution for 13(x)=4x^2-3x+7 equation:

13(x)=4x^2-3x+7

We move all terms to the left:

13(x)-(4x^2-3x+7)=0

We get rid of parentheses

-4x^2+13x+3x-7=0

We add all the numbers together, and all the variables

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

a = -4; b = 16; c = -7;
Δ = b2-4ac
Δ = 162-4·(-4)·(-7)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12}{2*-4}=\frac{-28}{-8}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12}{2*-4}=\frac{-4}{-8}
=1/2
$