10x2+4x+10=2x2+10x+15

Solution for 10x2+4x+10=2x2+10x+15 equation:

10x^2+4x+10=2x^2+10x+15

We move all terms to the left:

10x^2+4x+10-(2x^2+10x+15)=0

We get rid of parentheses

10x^2-2x^2+4x-10x-15+10=0

We add all the numbers together, and all the variables

8x^2-6x-5=0

a = 8; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·8·(-5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*8}=\frac{20}{16}
=1+1/4
$