2x^2+8x-14=3x-7

Solution for 2x^2+8x-14=3x-7 equation:

2x^2+8x-14=3x-7

We move all terms to the left:

2x^2+8x-14-(3x-7)=0

We get rid of parentheses

2x^2+8x-3x+7-14=0

We add all the numbers together, and all the variables

2x^2+5x-7=0

a = 2; b = 5; c = -7;
Δ = b2-4ac
Δ = 52-4·2·(-7)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-9}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+9}{2*2}=\frac{4}{4}
=1
$