X2+13x+5=4x-3

Solution for X2+13x+5=4x-3 equation:

X2+13X+5=4X-3

We move all terms to the left:

X2+13X+5-(4X-3)=0

We add all the numbers together, and all the variables

X^2+13X-(4X-3)+5=0

We get rid of parentheses

X^2+13X-4X+3+5=0

We add all the numbers together, and all the variables

X^2+9X+8=0

a = 1; b = 9; c = +8;
Δ = b2-4ac
Δ = 92-4·1·8
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*1}=\frac{-16}{2}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*1}=\frac{-2}{2}
=-1
$