5*x^2-20*x-103=37-5*x

Solution for 5*x^2-20*x-103=37-5*x equation:

5x^2-20x-103=37-5x

We move all terms to the left:

5x^2-20x-103-(37-5x)=0

We add all the numbers together, and all the variables

5x^2-20x-(-5x+37)-103=0

We get rid of parentheses

5x^2-20x+5x-37-103=0

We add all the numbers together, and all the variables

5x^2-15x-140=0

a = 5; b = -15; c = -140;
Δ = b2-4ac
Δ = -152-4·5·(-140)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-55}{2*5}=\frac{-40}{10}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+55}{2*5}=\frac{70}{10}
=7
$