4x^2+26x+42=90

Solution for 4x^2+26x+42=90 equation:

4x^2+26x+42=90

We move all terms to the left:

4x^2+26x+42-(90)=0

We add all the numbers together, and all the variables

4x^2+26x-48=0

a = 4; b = 26; c = -48;
Δ = b2-4ac
Δ = 262-4·4·(-48)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-38}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+38}{2*4}=\frac{12}{8}
=1+1/2
$