4x^2+10x=7

Solution for 4x^2+10x=7 equation:

4x^2+10x=7

We move all terms to the left:

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

a = 4; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·4·(-7)
Δ = 212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{53}}{2*4}=\frac{-10-2\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{53}}{2*4}=\frac{-10+2\sqrt{53}}{8}
$