5x^2-29x+20=8x+6

Solution for 5x^2-29x+20=8x+6 equation:

5x^2-29x+20=8x+6

We move all terms to the left:

5x^2-29x+20-(8x+6)=0

We get rid of parentheses

5x^2-29x-8x-6+20=0

We add all the numbers together, and all the variables

5x^2-37x+14=0

a = 5; b = -37; c = +14;
Δ = b2-4ac
Δ = -372-4·5·14
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-33}{2*5}=\frac{4}{10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+33}{2*5}=\frac{70}{10}
=7
$