6x^2+10x-20=8-7x

Solution for 6x^2+10x-20=8-7x equation:

6x^2+10x-20=8-7x

We move all terms to the left:

6x^2+10x-20-(8-7x)=0

We add all the numbers together, and all the variables

6x^2+10x-(-7x+8)-20=0

We get rid of parentheses

6x^2+10x+7x-8-20=0

We add all the numbers together, and all the variables

6x^2+17x-28=0

a = 6; b = 17; c = -28;
Δ = b2-4ac
Δ = 172-4·6·(-28)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*6}=\frac{14}{12}
=1+1/6
$