2x^2+5x-3=x+27

Solution for 2x^2+5x-3=x+27 equation:

2x^2+5x-3=x+27

We move all terms to the left:

2x^2+5x-3-(x+27)=0

We get rid of parentheses

2x^2+5x-x-27-3=0

We add all the numbers together, and all the variables

2x^2+4x-30=0

a = 2; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·2·(-30)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*2}=\frac{12}{4}
=3
$