x^2+10x-4=-x^2+3x

Solution for x^2+10x-4=-x^2+3x equation:

x^2+10x-4=-x^2+3x

We move all terms to the left:

x^2+10x-4-(-x^2+3x)=0

We get rid of parentheses

x^2+x^2-3x+10x-4=0

We add all the numbers together, and all the variables

2x^2+7x-4=0

a = 2; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·2·(-4)
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{-(7)-9}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+9}{2*2}=\frac{2}{4}
=1/2
$