4x^2-31x+103=3x^2+10x+7

Solution for 4x^2-31x+103=3x^2+10x+7 equation:

4x^2-31x+103=3x^2+10x+7

We move all terms to the left:

4x^2-31x+103-(3x^2+10x+7)=0

We get rid of parentheses

4x^2-3x^2-31x-10x-7+103=0

We add all the numbers together, and all the variables

x^2-41x+96=0

a = 1; b = -41; c = +96;
Δ = b2-4ac
Δ = -412-4·1·96
Δ = 1297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{1297}}{2*1}=\frac{41-\sqrt{1297}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{1297}}{2*1}=\frac{41+\sqrt{1297}}{2}
$