7x^2+10=101x-3x^2

Solution for 7x^2+10=101x-3x^2 equation:

7x^2+10=101x-3x^2

We move all terms to the left:

7x^2+10-(101x-3x^2)=0

We get rid of parentheses

7x^2+3x^2-101x+10=0

We add all the numbers together, and all the variables

10x^2-101x+10=0

a = 10; b = -101; c = +10;
Δ = b2-4ac
Δ = -1012-4·10·10
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-99}{2*10}=\frac{2}{20}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+99}{2*10}=\frac{200}{20}
=10
$